Как пишется единица давления

Единицы измерений, переводные таблицы и формулы

Units, Conversion Tables, and Formulas

Единицы измерения давления / Pressure 

Па, паскаль	кПа, килопаскаль	МПа, мегапаскаль	кгс/см², ат, техническая атмосфера	атм,  физическая атмосфера
Pa, pascal	kPa, kilopascal	MPa, megapascal	kgf/cm² или kp/cm², at, technical atmosphere	аtm,  atmosphere

бар	PSI или psi (фунт/кв. дюйм), фунт-сила на квадратный дюйм	мм рт. ст., миллиметр ртутного столба	мм вод. ст., миллиметр водяного столба
bar	PSI или psi (pounds/square inch или lbf/in²), pound-force per square inch	1 mm Hg	1 mm of water

Паскаль (Па, Pa)

Паскаль (Па, Pa) – единица измерения давления в Международной системе единиц измерения (система СИ). Единица названа в честь французского физика и математика Блеза Паскаля.

Паскаль равен давлению, вызываемому силой, равной одному ньютону (Н), равномерно распределённой по нормальной к ней поверхности площадью один квадратный метр:

1 паскаль (Па) ≡ 1 Н/м²

Кратные единицы образуют с помощью стандартных приставок СИ:

1 МПа (1 мегапаскаль) = 1000 кПа (1000 килопаскалей)

Атмосфера (физическая, техническая)

Атмосфера — внесистемная единица измерения давления, приблизительно равная атмосферному давлению на поверхности Земли на уровне Мирового океана.

Существуют две примерно равные друг другу единицы с таким названием:

1. Физическая, нормальная или стандартная атмосфера (атм, atm) — в точности равна 101 325 Па или 760 миллиметрам ртутного столба.

2. Техническая атмосфера (ат, at, кгс/см²) — равна давлению, производимому силой 1 кгс, направленной перпендикулярно и равномерно распределённой по плоской поверхности площадью 1 см² (98 066,5 Па).

   1 техническая атмосфера = 1 кгс/см² («килограмм-сила на сантиметр квадратный»). // 1 кгс = 9,80665 ньютонов (точно) ≈ 10 Н; 1 Н ≈ 0,10197162 кгс ≈ 0,1 кгс

На английском языке килограмм-сила обозначается как kgf (kilogram-force) или kp (kilopond) – килопонд, от латинского pondus, означающего вес.

Заметьте разницу: не pound (по-английски «фунт»), а pondus.

На практике приближенно принимают: 1 МПа = 10 атмосфер, 1 атмосфера = 0,1 МПа.

Бар

Бар (от греческого βάρος — тяжесть) — внесистемная единица измерения давления, примерно равная одной атмосфере. Один бар равен 105 Н/м² (или 0,1 МПа).

Соотношения между единицами давления

1 МПа = 10 бар = 10,19716 кгс/см² = 145,0377 PSI = 9,869233 (физ. атм.) =7500,7 мм рт.ст.

1 бар = 0,1 МПа = 1,019716 кгс/см² = 14,50377 PSI = 0,986923 (физ. атм.) =750,07 мм рт.ст.

1 ат (техническая атмосфера) = 1 кгс/см² (1 kp/cm², 1 kilopond/cm²) = 0,0980665 МПа = 0,98066 бар = 14,223

1 атм (физическая атмосфера) = 760 мм рт.ст.= 0,101325 МПа = 1,01325 бар = 1,0333 кгс/см²

1 мм ртутного столба = 133,32 Па =13,5951 мм водяного столба

Объемы жидкостей и газов / Volume

л (литр)	куб.м (кубический метр)	куб.см (кубический сантиметр)	кубический фут	кубический дюйм	галлон (США)	галлон (Англия)
l (liter)	cubic meter или cbm	cc или ccm	cubic feet или cu ft	cubic inch, cubic in, cu inch, cu in	gl или gallon (US)	gl или gallon (UK, Imperial)

1 gl (US) = 3,785 л

1 gl (Imperial) = 4,546 л

1 cu ft = 28,32 л = 0,0283 куб.м

1 cu in = 16,387 куб.см

Скорость потока / Flow

л/с (литр в секунду)	л/мин (литр в минуту)	куб.м/час (кубический метр в час)	кубический фут в минуту
l/s (liter/second)	l/min (liter/minute)	cbm/h (cubic meter/hour)	CFM или cfm (cubic feet/minute)

1 л/с = 60 л/мин = 3,6 куб.м/час = 2,119 cfm

1 л/мин = 0,0167 л/с = 0,06 куб.м/час = 0,0353 cfm

1 куб.м/час = 16,667 л/мин = 0,2777 л/с = 0,5885 cfm

1 cfm (кубический фут в минуту) = 0,47195 л/с = 28,31685 л/мин = 1,699011 куб.м/час

Пропускная способность / Valve flow characteristics

Коэффициент (фактор) расхода Kv

Flow Factor – Kv

Основным параметром запорного и регулирующего органа является коэффициент расхода Kv. Коэффициент расхода Kv показывает объем воды в куб.м/час (cbm/h) при температуре 5-30ºC, проходящей через затвор с потерей напора в 1 бар.

Коэффициент расхода Cv

Flow Coefficient – Cv

В странах с дюймовой системой измерений используется коэффициент Cv. Он показывает, какой расход воды в галлон/мин (gallon/minute, gpm) при температуре 60ºF проходит через арматуру при перепаде давления на арматуре в 1 psi.

Cv = 1,16 Kv

Kv = 0,853 Cv

Кинематическая вязкость / Viscosity

сСт  (сантистокс)	м²/с (квадратный метр в секунду)
cSt	m²/s

м²/с – единица кинематической вязкости в системе СИ

Стокс – единица кинематической вязкости в системе СГС

1 сСт = 1 мм²/с = 0,000001 м²/с

1 м²/с = 1000000 сСт

Единицы длины / Length

м (метр)	мм (миллиметр)	фут	дюйм
m	mm	ft (feet)	in (inch)

1 ft = 12 in = 0,3048 м

1 in = 0,0833 ft = 0,0254 м = 25,4 мм

1 м = 3,28083 ft = 39,3699 in

Единицы силы / Force

Н (ньютон)	кгс (килограмм-сила)	фунт-сила
N (newton)	kp (kilogram force)	lbf (pound force)

1 Н = 0,102 кгс = 0,2248 lbf

1 lbf = 0,454 кгс = 4,448 Н

1 кгс = 9,80665 Н (точно) ≈ 10 Н; 1 Н ≈ 0,10197162 кгс ≈ 0,1 кгс

На английском языке килограмм-сила обозначается как kgf (kilogram-force) или kp (kilopond) – килопонд, от латинского pondus, означающего вес. Обратите внимание: не pound (по-английски «фунт»), а pondus.

Единицы массы / Mass

г (грамм)	кг (килограмм)	фунт	унция
g	kg	lb (pound)	oz (ounce)

1 фунт = 16 унций = 453,59 г

            Момент силы (крутящий момент) / Torque

1 Нм (ньютон-метр)	1 кгсм (килограмм-сила-метр)	фунт-сила-фут
N * m	kp * m или kgf * m	lbf * ft

1 кгс . м = 9,81 Н . м = 7,233 фунт-сила-фут (lbf * ft)

Единицы измерения мощности / Power

Некоторые величины:

Ватт (Вт, W, 1 Вт = 1 Дж/с), лошадиная сила (л.с. – рус., hp или HP – англ., CV – франц., PS – нем.)

Соотношение единиц:

В России и некоторых других странах 1 л.с. (1 PS, 1 CV) = 75 кгс* м/с = 735,4988 Вт

В США, Великобритании и других странах 1 hp = 550 фут*фунт/с = 745,6999 Вт

Температура / Temperature

°C	K	°F
Градус Цельсия Celsius	Градус Кельвина Kelvin	Градус Фаренгейта Fahrenheit

Температура по шкале Фаренгейта:

[°F] = [°C] × 9⁄5 + 32

[°F] = [K] × 9⁄5 − 459,67

Температура по шкале Цельсия:

[°C] = [K] − 273,15

[°C] = ([°F] − 32) × 5⁄9

Температура по шкале Кельвина:

[K] = [°C] + 273.15

[K] = ([°F] + 459,67) × 5⁄9

Эта информация в формате doc.

Ниже представлена таблица с единицами измерения давления, включающая их названия, обозначения на английском (международном) и русском языках. Также отдельно приведено соотношение между перечисленными единицами.

• Единицы измерения давления

• Соотношение единиц измерения давления

Единицы измерения давления

Единица		Обозначение		Выражение через другие единицы
рус.	англ.	рус.	англ.
Паскаль	Pascal	Па	Pa	1 Па = 1 Н/м2 (или 1 Н · м-2)
Бар	Bar	бар	bar	1 бар = 105 Па = 1 ⋅ 106 дин/см2
Миллиметр ртутного столба	Millimetre of mercury	мм рт. ст. / торр	mm Hg / Torr	1 мм рт. ст. ≈ 133,3223684 Па
Физическая атмосфера	Standard atmosphere	атм	atm	1 атм = 101 325 Па
Техническая атмосфера	Technical atmosphere	ат	at	1 ат = 1 кгс/см2 = 98 066,5 Па
Метр водяного столба	Meter of water	м вод. ст. / м H2O	m H2O	1 м вод. ст. = 9806,65 Па
Фунт-сила на квадратный дюйм	Pound per square inch		psi / lb.p.sq.in.	1 psi = 1 lbf/in2 = 6894,75729 Па

Примечания:

• Из указанных единиц только Паскаль относится к международной системе СИ, поэтому все остальные единицы выражены через нее.
• Атмосферное давление, принятое за стандарт, равняется примерно 760 мм рт. ст. или 101 325 Па.
• psi (фунт-сила на квадратный дюйм) – внесистемная единица, которая в основном используется в США и Великобритании.

Соотношение единиц измерения давления

Единица	Па	бар	мм рт. ст.	атм	ат	м вод. ст.	psi
1 Па	1	10-5	7,5006 ⋅ 10-3	9,8692 ⋅ 10-6	10,197 ⋅ 10-6	1,0197 ⋅ 10-4	145,04 ⋅ 10-6
1 бар	105	1	750,06	0,98692	1,0197	10,197	14,504
1 мм рт. ст.	133,322	1,3332 ⋅ 10-3	1	1,3158 ⋅ 10-3	1,3595 ⋅ 10-3	13,595 ⋅ 10-3	19,337 ⋅ 10-3
1 атм	101325	1,01325	760	1	1,033	10,33	14,696
1 ат	98066,5	0,980665	735,56	0,96784	1	10	14,223
1 м вод. ст.	9806,65	9,80665 ⋅ 10-2	73,556	0,096784	0,1	1	1,4223
1 psi	6894,76	68,948 ⋅ 10-3	51,715	68,046 ⋅ 10-3	70,307 ⋅ 10-3	0,70307	1

Проект Карла III Ребане и хорошей компании		Раздел недели: Обезжиривающие водные растворы и органические растворители. Составы для очистки и обезжиривания поверхности.
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Единицы вакуума.    Поделиться:    Перевод единиц давления. Единицы величин давления и их соотношение. Таблица перевода единиц измерения давления. Па; МПа; бар; атм; мм рт.ст. = торр = тор; мм в.ст.; м в.ст., кг/см2; кгс/см2; psf; psi; дюймы рт.ст.; дюймы в.ст.               Версия для печати. Единица измерения давления в СИ- паскаль (русское обозначение: Па; международное: Pa) = Н/м2 Таблица перевода единиц измерения давления. Па; МПа; бар; атм; мм рт.ст.; мм в.ст.; м в.ст., кг/см 2; psf; psi; дюймы рт.ст.; дюймы в.ст. ниже Обратите внимание, тут 2 таблицы и список. Вот еще полезная ссылка: Плотность воды в зависимости от температуры (и другие параметры) Таблица перевода единиц измерения давления. Па; МПа; бар; атм; мм рт.ст.; мм в.ст.; м в.ст., кг/см 2; psf; psi; дюймы рт.ст.; дюймы в.ст. Соотношение единиц измерения давления. Для того, чтобы перевести давление в единицах: В единицы: Па (Н/м2) МПа bar atmosphere мм рт. ст. мм в.ст. м в.ст. кгс/см2 Следует умножить на: Па (Н/м2) — паскаль, единица давления СИ 1 1*10-6 10-5 9.87*10-6 0.0075 0.1 10-4 1.02*10-5 МПа, мегапаскаль 1*106 1 10 9.87 7.5*103 105 102 10.2 бар 105 10-1 1 0.987 750 1.0197*104 10.197 1.0197 атм, атмосфера 1.01*105 1.01* 10-1 1.013 1 759.9 10332 10.332 1.03 мм рт. ст., мм ртутного столба 133.3 133.3*10-6 1.33*10-3 1.32*10-3 1 13.3 0.013 1.36*10-3 мм в.ст., мм водяного столба 10 10-5 0.000097 9.87*10-5 0.075 1 0.001 1.02*10-4 м в.ст., метр водяного столба 104 10-2 0.097 9.87*10-2 75 1000 1 0.102 кгс/см2 , килограмм-сила на квадратный сантиметр 9.8*104 9.8*10-2 0.98 0.97 735 10000 10 1 фунтов на кв. фут / pound square feet (psf) 47.8 4.78*10-5 4.78*10-4 4.72*10-4 0.36 4.78 4.78 10-3 4.88*10-4 фунтов на кв. дюйм / pound square inches (psi) 6894.76 6.89476*10-3 0.069 0.068 51.7 689.7 0.690 0.07 Дюймов рт.ст. / inches Hg 3377 3.377*10-3 0.0338 0.033 25.33 337.7 0.337 0.034 Дюймов в.ст. / inches H2O 248.8 2.488*10-2 2.49*10-3 2.46*10-3 1.87 24.88 0.0249 0.0025 Таблица перевода единиц измерения давления. Па; МПа; бар; атм; мм рт.ст.; мм в.ст.; м в.ст., кг/см 2; psf; psi; дюймы рт.ст.; дюймы в.ст. Для того, чтобы перевести давление в единицах: В единицы: фунтов на кв. фут / pound square feet (psf) фунтов на кв. дюйм / pound square inches (psi) Дюймов рт.ст. / inches Hg Дюймов в.ст. / inches H2O Следует умножить на: Па (Н/м2) — единица давления СИ 0.021 1.450326*10-4 2.96*10-4 4.02*10-3 МПа 2.1*104 1.450326*102 2.96*102 4.02*103 бар 2090 14.50 29.61 402 атм 2117.5 14.69 29.92 407 мм рт. ст. 2.79 0.019 0.039 0.54 мм в.ст. 0.209 1.45*10-3 2.96*10-3 0.04 м в.ст. 209 1.45 2.96 40.2 кгс/см2 2049 14.21 29.03 394 фунтов на кв. фут / pound square feet (psf) 1 0.0069 0.014 0.19 фунтов на кв. дюйм / pound square inches (psi) 144 1 2.04 27.7 Дюймов рт.ст. / inches Hg 70.6 0.49 1 13.57 Дюймов в.ст. / inches H2O 5.2 0.036 0.074 1 Подробный список единиц давления, один паскаль это: 1 Па (Н/м2) = 0.0000102 Атмосфера «метрическая» / Atmosphere (metric) 1 Па (Н/м2) = 0.0000099 Атмосфера стандартная Atmosphere (standard) = Standard atmosphere 1 Па (Н/м2) = 0.00001 Бар / Bar 1 Па (Н/м2) = 10 Барад / Barad 1 Па (Н/м2) = 0.0007501 Сантиметров рт. ст. (0 °C) 1 Па (Н/м2) = 0.0101974 Сантиметров во. ст. (4 °C) 1 Па (Н/м2) = 10 Дин/квадратный сантиметр 1 Па (Н/м2) = 0.0003346 Футов водяного столба / Foot of water (4 °C) 1 Па (Н/м2) = 10-9 Гигапаскалей 1 Па (Н/м2) = 0.01 Гектопаскалей 1 Па (Н/м2) = 0.0002953 Дюмов рт.ст. / Inch of mercury (0 °C) 1 Па (Н/м2) = 0.0002961 Дюймов рт. ст. / Inch of mercury (15.56 °C) 1 Па (Н/м2) = 0.0040186 Дюмов в.ст. / Inch of water (15.56 °C) 1 Па (Н/м2) = 0.0040147 Дюмов в.ст. / Inch of water (4 °C) 1 Па (Н/м2) = 0.0000102 кгс/см2 / Kilogram force/centimetre2 1 Па (Н/м2) = 0.0010197 кгс/дм2 / Kilogram force/decimetre2 1 Па (Н/м2) = 0.101972 кгс/м2 / Kilogram force/meter2 1 Па (Н/м2) = 10-7 кгс/мм2 / Kilogram force/millimeter2 1 Па (Н/м2) = 10-3 кПа 1 Па (Н/м2) = 10-7 Килофунтов силы/ квадратный дюйм / Kilopound force/square inch 1 Па (Н/м2) = 10-6 МПа 1 Па (Н/м2) = 0.000102 Метров в.ст. / Meter of water (4 °C) 1 Па (Н/м2) = 10 Микробар / Microbar (barye, barrie) 1 Па (Н/м2) = 7.50062 Микронов рт.ст. / Micron of mercury (millitorr) 1 Па (Н/м2) = 0.01 Милибар / Millibar 1 Па (Н/м2) = 0.0075006 Миллиметров рт.ст / Millimeter of mercury (0 °C) 1 Па (Н/м2) = 0.10207 Миллиметров в.ст. / Millimeter of water (15.56 °C) 1 Па (Н/м2) = 0.10197 Миллиметров в.ст. / Millimeter of water (4 °C) 1 Па (Н/м2) =7.5006 Миллиторр / Millitorr 1 Па (Н/м2) = 1Н/м2/ Newton/square meter 1 Па (Н/м2) = 32.1507 Повседневных унций / кв. дюйм / Ounce force (avdp)/square inch 1 Па (Н/м2) = 0.0208854 Фунтов силы на кв. фут / Pound force/square foot 1 Па (Н/м2) = 0.000145 Фунтов силы на кв. дюйм / Pound force/square inch 1 Па (Н/м2) = 0.671969 Паундалов на кв. фут / Poundal/square foot 1 Па (Н/м2) = 0.0046665 Паундалов на кв. дюйм / Poundal/square inch 1 Па (Н/м2) = 0.0000093 Длинных тонн на кв. фут / Ton (long)/foot2 1 Па (Н/м2) = 10-7 Длинных тонн на кв. дюйм / Ton (long)/inch2 1 Па (Н/м2) = 0.0000104 Коротких тонн на кв. фут / Ton (short)/foot2 1 Па (Н/м2) = 10-7 Тонн на кв. дюйм / Ton/inch2 1 Па (Н/м2) = 0.0075006 Торр / Torr давление в паскалях и атмосферах, перевести давление в паскали атмосферное давление равно ХХХ мм.рт.ст. выразите его в паскалях единицы давления газа — перевод единицы давления жидкости — перевод Куча единиц измерения от Проекта dpva.ru — поможет, если встретились незнакомые величины. 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Давление —

физическая величина, численно равная силе, действующей на единицу площади поверхности перпендикулярно этой поверхности.

Перевод единиц измерения давления онлайн.

Единицы измерения.

• Паскаль — единица измерения давления в СИ. Обозначение в России: Па; международное: Pa. Единицы измерения Па  определяются выражением (P=F/S, Н/м²). Данная единица измерения широко применяется при инженерных расчетах, в современной справочной литературе, в обозначение параметров оборудования, технических устройств, при разработке проектной и рабочей документации;
• бар — внесистемные единицы измерения. Обозначение в России: бар; международное: bar. Один бар равен 10⁵ Па.  Данная единица измерения широко применяется при  обозначение и выборе параметров оборудования, технических устройств;
• миллибар — внесистемные единицы измерения. Обозначение на сайте: мбар. Данная единица измерения широко применяется при  обозначение и выборе параметров оборудования, технических устройств (встречает в документации на оборудование иностранного образца);
• мм рт. ст. — внесистемная единица измерения давления. Обозначение в России: мм рт. ст.; международное: mm Hg.  Миллиметр рту́тного столба́ равен 101 325 / 760 ≈ 133,3223684 Па;
• мм вод. ст. — внесистемная единица измерения давления. Обозначение в России: мм вод. ст., мм H2O; международное: mm H2O. Миллиметр водяного столба́ равен гидростатическому давлению столба воды высотой 1 мм, оказываемому на плоское основание при температуре воды 4 °С. В Российской Федерации допущен к использованию в качестве внесистемной единицы измерения давления без ограничения срока с областью использования «все области»;
• атмосфера — внесистемная единица измерения давления, приблизительно равная атмосферному давлению на поверхности Земли на уровне Мирового океана. Различают  техническую и физическую (нормальная, стандартная) атмосферу. В Российской Федерации к использованию в качестве внесистемной единицы допущена только техническая атмосфера с областью применения «все области». Обозначение в России:  ат; международное: at. Существовавшее ранее ограничение срока действия допуска 2016 годом отменено в августе 2015 года. Техническая атмосфера равна давлению, производимому силой в 1 кгс, равномерно распределённой по перпендикулярной к ней плоской поверхности площадью 1 см². В справочной литературе и старой документации встречаются так же (на данный момент не используются):
  • ати — избыточной давление;
  • ата — абсолютное давление;
• килограмм-силы на см² — единица давления в системе единиц МКГСС (система единиц измерения, в которой основными единицами являются метр, килограмм-сила и секунд). Обозначение в России:  кгс/см². В Российской Федерации допущена к использованию в качестве внесистемных единиц без ограничения срока действия с областью применения «все области». Килограмм-сила равна силе, сообщающей телу  массой один килограмм  ускорение 9,80665 м/с².

Перевод единиц измерения давления (в табличном виде).

Переводимые единицы  давления	Перевод давления в единицы:
Пa	кПа	МПа	бар	мбар	мм рт. ст.	мм вод. ст.	м вод. ст.	ат	кгс/см2
Па	1	10-3	10-6	10-5	10-2	0.0075	0.1	10-4	9.87*10-5	1.02*10-5
кПа	103	1	10—3	10-2	10	7.5	103	10-1	9.87*10-2	1.02*10-3
МПа	106	103	1	10	104	7.5*103	105	102	9.87	10.2
бар	105	102	10-1	1	103	750	1.0197*104	10.197	0.987	1.0197
мбар	102	0.1	10-4	0.001	1	0.750	10.197	10.197*10-2	0.987*10-3	1.0197*10-3
мм рт. ст.	133.3	133.3*10-3	133.3*10-6	1.33*10-3	1.33	1	13.3	0.013	1.32*10-3	1.36*10-3
мм вод. ст.	10	10-2	10-5	9.7*10-5	0.097	0.075	1	0.001	9.87*10-5	1.02*10-4
м вод. ст.	104	10	10-2	0.097	97	75	1000	1	9.87*10-2	0.102
ат	1.01*105	1.01*102	1.01* 10-1	1.013	1013	759.9	10332	10.332	1	1.03
кгс/см2	9.8*104	9.8*10	9.8*10-2	0.98	980	735	10000	10	0.9708	1

Порядки единиц измерения давления.

Порядок единиц измерения	Единицы измерения
Па	ат	мм рт. ст.	мм вод. ст.	кгс/м2	бар	мбар
10	даПa	—	см рт. cт.	см вод. cт.	—	—	—
1 00	ГПa	—	—	—	—	—	—
1 000	кПa	—	м рт. cт.	м вод. cт.	—	—	бар
10 000	—	—	—	—	кгc/cм2
1 000 000	МПa	—	—	—	—	—

Виды давления.

Различают три основных вида давления:

• вакуумметрическое давление;
• избыточной давление;
• абсолютное давление.

Вид давления непосредственно связан со сравнением его относительно атмосферного давления (Р_ат).  или с использованием атмосферного давления.

Избыточное давление (Р_изб) это величина показывающие на сколько давление в оборудовании или трубопроводе выше атмосферного давления.  Т.е. если давление измеряют относительно атмосферного давления, то такое давление называется избыточным. Избыточное давление измеряется с помощью манометров.

Избыточное давление широко применяется в эксплуатации, в том числе:

• • при выборе и подборе  оборудования по паспортным данным;
  • при различных классификациях оборудования и трубопроводов на стадиях проектирования и монтажа;
  • при нанесении маркировки на оборудование и трубопроводы.

Абсолютное давление (Р_абс) это величина давления с учетом действующего атмосферного давления, т.е.:

Р_абс=Р_изб + Р_ат;

Другим словами, если давление определяют относительно давления равного 0, то  измеренное давление называют абсолютным.

Абсолютное давление применяется в основном инженерно-техническим персоналом (ИТР) при инженерных расчетах и  в расчетах  при выборе оборудования (основных на применении абсолютного давления). Ярким примером использования абсолютного давления в расчетах служит уравнение состояния идеального газа.

Примером использования абсолютного давления являются:

• • подбор счетчиков на трубопроводах с газовыми средами (в том числе водяного пара);
  • гидравлические расчеты трубопроводов газов (в том числе водяного пара);
  • расчеты на прочность оборудования и трубопроводов с газовыми средами (в том числе водяной пар);
  • и т.д.

В случаях когда атмосферное давления больше абсолютного давления речь идет о вакуумметрическом давлении (Р_вак). Т.е.  вакуумметрическое давление это величина давления показывающая на сколько атмосферное давления больше абсолютного давления.

Р_вак=Р_ат  — Р_абс;

Вакуум широко применяется в технологических процессах на промышленных предприятиях. На всех этих объектах применяется вакуумметрическое давление на стадиях проектирования, монтажа и эксплуатации.

Дополнительная классификация  давления в инженерных расчетах.

• • гидростатическое давление (P_g) — давление столба жидкости (газа) над условным уровнем;

Это давление создаваемое  собственным весом жидкости (газа) в определенном сечении, то есть:

P_g=F_g/S, где F_g — вес столба жидкости (газа), S — площадь сечения.

Другая наиболее распространения форма записи гидростатического давления (после преобразования) представляет из себя формулу:

P_g=ρgh, где ρ — плотность жидкости (газа), g — ускорение свободного падения, h — высота столба жидкости (газа).

Гидростатического давления учитывается при расчет открытых систем (связанных с атмосферой). В открытых системах низкого давления учитывать необходимо обязательно  (например: вентиляция, системы дымоудаления, газопроводы низкого давления и т.д.).

Примерами гидростатического давления могут служить  атмосферное давление, различные гидравлические затворы (например гидрозатвор на деаэраторе), использующие вес водяного столба для предохранения от повышения давления в системы выше допустимого.

Рассчитать гидростатическое давление можно в отдельной теме.

• • естественное давление (P_e) — вызывается разностью гидростатических давлений двух столбов жидкости (газов) высотой h, имеющей различную среднюю плотность. При расчетах естественное давление обычно учитывают в системах низкого давления (например: естественная вытяжная вентиляция);

Естественное давление обычно рассчитывают по формуле (выведенной из разности гидростатических давлений в двух сечения с разной плотностью):

P_e =( ρ₁ — ρ₂)gh_e,

где ρ₁  — плотность жидкости (газа) в 1-ом сечении, ρ₂  — плотность жидкости (газа) в 1-ом сечении, h_e — разность высотных отметок двух сечений.

Рассчитать естественное давление можно в отдельной теме.

• • парциальное давление (P_p)  — называют давление, которое оказывает отдельно взятый компонент из газовой смеси (например, на колбу, баллон или границу атмосферы) исходя из того, что он один займет весь объем смеси при той же температуре. Понятие парциального давления широко используется в химии. Возможно определение парциального давления по уравнению состояния идеального газа при заданном общем объеме смеси и той же температуре. Общее давление смеси газов определяется, как суммам парциальных давлений отдельных компонентов смеси.
  • потери давления (ΔP) — называют давление, равное разности давлений в двух сечениях системы. Разность давления обуславливается в основном потерями на преодоления сопротивления при движении вещества  в системе (возможно участие естественного и гидростатического давления). Различают сопротивления: путевые и местные.  Путевые сопротивления связанны с преодолением трения в системе. Местные сопротивления связаны с изменением скорости движения или направления потока. Потери давления определяются расчетным методом в процессе выполнения гидравлического или аэродинамического расчета системы. Например: гидравлический расчет газопроводов природного газа.
  • разряжение (или тяга) — снижение давления в системе, способствующее притоку среды в область пониженного давления.  Может быть естественное или принудительное. Примерами использования разряжения (тяги) служат:
    • системы естественной вентиляции;
    • системы механического дымоудаления (перед дымососам);
    • различные системы инжекции (элеваторы в системах отопления, инжекционные газовые горелки и т.д. ), основанные на уменьшении давления в сечении за счет уменьшения площади сечения и увеличении скорости истечения в нем.

Видеоматериал по теме давление и виды давления:

Приборы измерения давления.

Для измерения давления используются измерительные приборы под общим названием — манометры (согласно ГОСТ 8.271-77 манометр это измерительный прибор или измерительная установка для измерения давления или разности давлений). Но в практике сложилось ассоциировать манометры с измерением избыточного давления.

Общая классификация манометров.

• • по типу измеряемого давления;
  • по принципу действия;
  • по классу точности;
  • по назначению.

По типу измеряемого давления.

Основные виды измеряемого давления разобраны выше. Типы измеряемых давлений шире и содержит производные типы от основных:

• • манометр абсолютного давления;
  • барометр (манометр абсолютного давления для измерения давления околоземной атмосферы), в том числе барограф (барометр с непрерывной записью);
  • манометр избыточного давления (обычно просто манометр), в том числе напоромер (манометр избыточного давления в газовых средах с верхним пределом измерения не более 40000 Па /4000 кгс/м² );
  • вакуумметр (манометр для измерения давления разреженного газа) , в том числе тягомер (вакуумметр для измерения давления разреженного газа с верхним пределом измерения не более 40000 Па/4000 кгс/м²);
  • мановакуумметр (манометр, для измерения избыточного давления и давления разреженного газа), в том числе тягонапоромер (мановакуумметр для газовых сред с верхним пределом измерения не более 20000 Па/2000 кгс/м²);
  • дифференциальный манометр (манометр для измерения разности двух давлений), в том числе микроманометр (дифманометр с верхним пределом измерения не более 40000 Па/4000 кгс/м²);
  • измеритель парциальных давлений (манометр для измерения давления, которое оказывал бы один из газов, входящих в газовую смесь, если бы из нее были удалены остальные газы, при условии сохранения первоначальных объема и температуры).

По принципу действия.

По принципу действия манометров общий список классификации включает:

• • жидкостный манометр;
  • U-образный манометр;
  • компрессионный манометр;
  • колокольный манометр;
  • кольцевой манометр;
  • грузопоршневой манометр;
  • деформационный манометр;
  • мембранный манометр;
  • сильфонный манометр;
  • трубчато-пружинный манометр;
  • манометр с вялой мембраной;
  • электрический манометр;
  • пьезоэлектрический манометр;
  • манометр сопротивления;
  • ионизационный манометр;
  • электронный ионизационный манометр;
  • магнитный электроразрядный манометр;
  • радиоизотопный манометр;
  • тепловой манометр;
  • термопарный манометр;
  • вязкостный манометр.

В промышленности широко применяются следующие типы манометров:

• • жидкостные манометры.
  • грузопоршневые манометры.
  • трубчато-пружинный манометры.

Жидкостные манометров — манометр, принцип действия которого основан на уравновешивании измеряемого давления, или разности давлений, давлением столба жидкости.

Грузопоршневые манометры — манометр, принцип действия которого основан на уравновешивании измеряемого давления давлением, создаваемым весом поршня с грузоприемным устройством, и грузов с учетом сил жидкостного трения.

Трубчато-пружинный манометры- деформационный манометр, в котором чувствительным элементом является трубчатая пружина.

Видеоматериал по теме типы манометров:

По классу точности.

Манометры точности измерения согласно ГОСТ 8.271-77 «Манометры, вакуумметры, мановакуумметры, напоромеры, тягомеры и тягонапоромеры. Общие технические условия» классифицируются на несколько классов точности:

• • 0,4*;
  • 0,6;
  • 1,0;
  • 1,5;
  • 2,5;
  • 4,0*.

Примечание: * Устанавливается по заказу потребителя.

Класс точности манометра отражает пределы допустимой основной погрешности в % от диапазона показания шкалы.

Нормы (ГОСТ) устанавливает зависимость диаметра или размера лицевой панели корпуса манометру классу точности:

По назначению.

Манометры в зависимости от области применения и рабочей среду по назначению классифицируются:

• • общетехнические, общепромышленные;
  • специальные манометры;
  • судовые манометры;
  • железнодорожные манометры.

Манометры в зависимости от способа фиксации давления классифицируются:

• • показывающие;
  • самопишущие манометры;
  • электроконтактные манометры.

В зависимости от метрологического назначения манометры делятся:

• • на образцовые (эталонные);
  • рабочие;

Калькуляторы давления.

Расчет давления (классическая формула).

Расчет абсолютного давления.

Поделиться ссылкой:

This article is about pressure in the physical sciences. For other uses, see Pressure (disambiguation).

Pressure
Common symbols	p, P
SI unit	pascal [Pa]
In SI base units	1 N/m2, 1 kg/(m·s2), or 1 J/m3
Derivations from other quantities	p = F / A
Dimension	M L−1 T−2

Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.^[1]: 445 Gauge pressure (also spelled gage pressure)^[a] is the pressure relative to the ambient pressure.

Various units are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the SI unit of pressure, the pascal (Pa), for example, is one newton per square metre (N/m²); similarly, the pound-force per square inch (psi, symbol lbf/in²) is the traditional unit of pressure in the imperial and U.S. customary systems. Pressure may also be expressed in terms of standard atmospheric pressure; the atmosphere (atm) is equal to this pressure, and the torr is defined as 1⁄760 of this. Manometric units such as the centimetre of water, millimetre of mercury, and inch of mercury are used to express pressures in terms of the height of column of a particular fluid in a manometer.

Definition[edit]

Pressure is the amount of force applied perpendicular to the surface of an object per unit area. The symbol for it is «p» or P.^[2]
The IUPAC recommendation for pressure is a lower-case p.^[3]
However, upper-case P is widely used. The usage of P vs p depends upon the field in which one is working, on the nearby presence of other symbols for quantities such as power and momentum, and on writing style.

Formula[edit]

Mathematically:

^[4]

where:

is the pressure,

is the magnitude of the normal force,

is the area of the surface on contact.

Pressure is a scalar quantity. It relates the vector area element (a vector normal to the surface) with the normal force acting on it. The pressure is the scalar proportionality constant that relates the two normal vectors:

The minus sign comes from the convention that the force is considered towards the surface element, while the normal vector points outward. The equation has meaning in that, for any surface S in contact with the fluid, the total force exerted by the fluid on that surface is the surface integral over S of the right-hand side of the above equation.

It is incorrect (although rather usual) to say «the pressure is directed in such or such direction». The pressure, as a scalar, has no direction. The force given by the previous relationship to the quantity has a direction, but the pressure does not. If we change the orientation of the surface element, the direction of the normal force changes accordingly, but the pressure remains the same.^{[citation needed]}

Pressure is distributed to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. It is a fundamental parameter in thermodynamics, and it is conjugate to volume.^[5]

Units[edit]

The SI unit for pressure is the pascal (Pa), equal to one newton per square metre (N/m², or kg·m⁻¹·s⁻²). This name for the unit was added in 1971;^[6] before that, pressure in SI was expressed simply in newtons per square metre.

Other units of pressure, such as pounds per square inch (lbf/in²) and bar, are also in common use. The CGS unit of pressure is the barye (Ba), equal to 1 dyn·cm⁻², or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre (g/cm² or kg/cm²) and the like without properly identifying the force units. But using the names kilogram, gram, kilogram-force, or gram-force (or their symbols) as units of force is expressly forbidden in SI. The technical atmosphere (symbol: at) is 1 kgf/cm² (98.0665 kPa, or 14.223 psi).

Pressure is related to energy density and may be expressed in units such as joules per cubic metre (J/m³, which is equal to Pa).
Mathematically:

Some meteorologists prefer the hectopascal (hPa) for atmospheric air pressure, which is equivalent to the older unit millibar (mbar). Similar pressures are given in kilopascals (kPa) in most other fields, except aviation where the hecto- prefix is commonly used. The inch of mercury is still used in the United States. Oceanographers usually measure underwater pressure in decibars (dbar) because pressure in the ocean increases by approximately one decibar per metre depth.

The standard atmosphere (atm) is an established constant. It is approximately equal to typical air pressure at Earth mean sea level and is defined as 101325 Pa.

Because pressure is commonly measured by its ability to displace a column of liquid in a manometer, pressures are often expressed as a depth of a particular fluid (e.g., centimetres of water, millimetres of mercury or inches of mercury). The most common choices are mercury (Hg) and water; water is nontoxic and readily available, while mercury’s high density allows a shorter column (and so a smaller manometer) to be used to measure a given pressure. The pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation p = ρgh, where g is the gravitational acceleration. Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column does not define pressure precisely. When millimetres of mercury (or inches of mercury) are quoted today, these units are not based on a physical column of mercury; rather, they have been given precise definitions that can be expressed in terms of SI units.^[7] One millimetre of mercury is approximately equal to one torr. The water-based units still depend on the density of water, a measured, rather than defined, quantity. These manometric units are still encountered in many fields. Blood pressure is measured in millimetres of mercury in most of the world, and lung pressures in centimetres of water are still common.^{[citation needed]}

Underwater divers use the metre sea water (msw or MSW) and foot sea water (fsw or FSW) units of pressure, and these are the standard units for pressure gauges used to measure pressure exposure in diving chambers and personal decompression computers. A msw is defined as 0.1 bar (= 100000 Pa = 10000 Pa), is not the same as a linear metre of depth. 33.066 fsw = 1 atm^{[citation needed]} (1 atm = 101325 Pa / 33.066 = 3064.326 Pa). Note that the pressure conversion from msw to fsw is different from the length conversion: 10 msw = 32.6336 fsw, while 10 m = 32.8083 ft.^{[citation needed]}

Gauge pressure is often given in units with «g» appended, e.g. «kPag», «barg» or «psig», and units for measurements of absolute pressure are sometimes given a suffix of «a», to avoid confusion, for example «kPaa», «psia». However, the US National Institute of Standards and Technology recommends that, to avoid confusion, any modifiers be instead applied to the quantity being measured rather than the unit of measure.^[8] For example, «p_g = 100 psi» rather than «p = 100 psig».

Differential pressure is expressed in units with «d» appended; this type of measurement is useful when considering sealing performance or whether a valve will open or close.

Presently or formerly popular pressure units include the following:

• atmosphere (atm)
• manometric units:
  • centimetre, inch, millimetre (torr) and micrometre (mTorr, micron) of mercury,
  • height of equivalent column of water, including millimetre (mm H
    ₂O), centimetre (cm H
    ₂O), metre, inch, and foot of water;
• imperial and customary units:
  • kip, short ton-force, long ton-force, pound-force, ounce-force, and poundal per square inch,
  • short ton-force and long ton-force per square inch,
  • fsw (feet sea water) used in underwater diving, particularly in connection with diving pressure exposure and decompression;
• non-SI metric units:
  • bar, decibar, millibar,
    • msw (metres sea water), used in underwater diving, particularly in connection with diving pressure exposure and decompression,
  • kilogram-force, or kilopond, per square centimetre (technical atmosphere),
  • gram-force and tonne-force (metric ton-force) per square centimetre,
  • barye (dyne per square centimetre),
  • kilogram-force and tonne-force per square metre,
  • sthene per square metre (pieze).

Examples[edit]

As an example of varying pressures, a finger can be pressed against a wall without making any lasting impression; however, the same finger pushing a thumbtack can easily damage the wall. Although the force applied to the surface is the same, the thumbtack applies more pressure because the point concentrates that force into a smaller area. Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. Unlike stress, pressure is defined as a scalar quantity. The negative gradient of pressure is called the force density.^[9]

Another example is a knife. If we try to cut with the flat edge, force is distributed over a larger surface area resulting in less pressure, and it will not cut. Whereas using the sharp edge, which has less surface area, results in greater pressure, and so the knife cuts smoothly. This is one example of a practical application of pressure^[10]

For gases, pressure is sometimes measured not as an absolute pressure, but relative to atmospheric pressure; such measurements are called gauge pressure. An example of this is the air pressure in an automobile tire, which might be said to be «220 kPa (32 psi)», but is actually 220 kPa (32 psi) above atmospheric pressure. Since atmospheric pressure at sea level is about 100 kPa (14.7 psi), the absolute pressure in the tire is therefore about 320 kPa (46 psi). In technical work, this is written «a gauge pressure of 220 kPa (32 psi)». Where space is limited, such as on pressure gauges, name plates, graph labels, and table headings, the use of a modifier in parentheses, such as «kPa (gauge)» or «kPa (absolute)», is permitted. In non-SI technical work, a gauge pressure of 32 psi (220 kPa) is sometimes written as «32 psig», and an absolute pressure as «32 psia», though the other methods explained above that avoid attaching characters to the unit of pressure are preferred.^[8]

Gauge pressure is the relevant measure of pressure wherever one is interested in the stress on storage vessels and the plumbing components of fluidics systems. However, whenever equation-of-state properties, such as densities or changes in densities, must be calculated, pressures must be expressed in terms of their absolute values. For instance, if the atmospheric pressure is 100 kPa (15 psi), a gas (such as helium) at 200 kPa (29 psi) (gauge) (300 kPa or 44 psi [absolute]) is 50% denser than the same gas at 100 kPa (15 psi) (gauge) (200 kPa or 29 psi [absolute]). Focusing on gauge values, one might erroneously conclude the first sample had twice the density of the second one.^{[citation needed]}

Scalar nature[edit]

In a static gas, the gas as a whole does not appear to move. The individual molecules of the gas, however, are in constant random motion. Because we are dealing with an extremely large number of molecules and because the motion of the individual molecules is random in every direction, we do not detect any motion. When the gas is at least partially confined (that is, not free to expand rapidly), the gas will exhibit a static pressure. This confinement can be achieved with either a physical container of some sort, or in a gravitational well such as a planet, otherwise known as atmospheric pressure. In a physical container, the pressure of the gas originates from the molecules colliding with the walls of the container. We can put the walls of our container anywhere inside the gas, and the force per unit area (the pressure) is the same. We can shrink the size of our «container» down to a very small point (becoming less true as we approach the atomic scale), and the pressure will still have a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has magnitude but no direction sense associated with it. Pressure force acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular (at right angle) to the surface.^{[citation needed]}

A closely related quantity is the stress tensor σ, which relates the vector force to the
vector area via the linear relation .

This tensor may be expressed as the sum of the viscous stress tensor minus the hydrostatic pressure. The negative of the stress tensor is sometimes called the pressure tensor, but in the following, the term «pressure» will refer only to the scalar pressure.^{[citation needed]}

According to the theory of general relativity, pressure increases the strength of a gravitational field (see stress–energy tensor) and so adds to the mass-energy cause of gravity. This effect is unnoticeable at everyday pressures but is significant in neutron stars, although it has not been experimentally tested.^[11]

Types[edit]

Fluid pressure[edit]

Fluid pressure is most often the compressive stress at some point within a fluid. (The term fluid refers to both liquids and gases – for more information specifically about liquid pressure, see section below.)

Fluid pressure occurs in one of two situations:

1. An open condition, called «open channel flow», e.g. the ocean, a swimming pool, or the atmosphere.
2. A closed condition, called «closed conduit», e.g. a water line or gas line.

Pressure in open conditions usually can be approximated as the pressure in «static» or non-moving conditions (even in the ocean where there are waves and currents), because the motions create only negligible changes in the pressure. Such conditions conform with principles of fluid statics. The pressure at any given point of a non-moving (static) fluid is called the hydrostatic pressure.

Closed bodies of fluid are either «static», when the fluid is not moving, or «dynamic», when the fluid can move as in either a pipe or by compressing an air gap in a closed container. The pressure in closed conditions conforms with the principles of fluid dynamics.

The concepts of fluid pressure are predominantly attributed to the discoveries of Blaise Pascal and Daniel Bernoulli. Bernoulli’s equation can be used in almost any situation to determine the pressure at any point in a fluid. The equation makes some assumptions about the fluid, such as the fluid being ideal^[12] and incompressible.^[12] An ideal fluid is a fluid in which there is no friction, it is inviscid^[12] (zero viscosity).^[12] The equation for all points of a system filled with a constant-density fluid is^[13]

where:

p, pressure of the fluid,

= ρg, density × acceleration of gravity is the (volume-) specific weight of the fluid,^[12]

v, velocity of the fluid,

g, acceleration of gravity,

z, elevation,

, pressure head,

, velocity head.

Applications[edit]

• Hydraulic brakes
• Artesian well
• Blood pressure
• Hydraulic head
• Plant cell turgidity
• Pythagorean cup
• Pressure washing

Explosion or deflagration pressures[edit]

Explosion or deflagration pressures are the result of the ignition of explosive gases, mists, dust/air suspensions, in unconfined and confined spaces.

Negative pressures[edit]

While pressures are, in general, positive, there are several situations in which negative pressures may be encountered:

• When dealing in relative (gauge) pressures. For instance, an absolute pressure of 80 kPa may be described as a gauge pressure of −21 kPa (i.e., 21 kPa below an atmospheric pressure of 101 kPa). For example, abdominal decompression is an obstetric procedure during which negative gauge pressure is applied intermittently to a pregnant woman’s abdomen.
• Negative absolute pressures are possible. They are effectively tension, and both bulk solids and bulk liquids can be put under negative absolute pressure by pulling on them.^[14] Microscopically, the molecules in solids and liquids have attractive interactions that overpower the thermal kinetic energy, so some tension can be sustained. Thermodynamically, however, a bulk material under negative pressure is in a metastable state, and it is especially fragile in the case of liquids where the negative pressure state is similar to superheating and is easily susceptible to cavitation.^[15] In certain situations, the cavitation can be avoided and negative pressures sustained indefinitely,^[15] for example, liquid mercury has been observed to sustain up to −425 atm in clean glass containers.^[16] Negative liquid pressures are thought to be involved in the ascent of sap in plants taller than 10 m (the atmospheric pressure head of water).^[17]
• The Casimir effect can create a small attractive force due to interactions with vacuum energy; this force is sometimes termed «vacuum pressure» (not to be confused with the negative gauge pressure of a vacuum).
• For non-isotropic stresses in rigid bodies, depending on how the orientation of a surface is chosen, the same distribution of forces may have a component of positive pressure along one surface normal, with a component of negative pressure acting along another surface normal.
  • The stresses in an electromagnetic field are generally non-isotropic, with the pressure normal to one surface element (the normal stress) being negative, and positive for surface elements perpendicular to this.
• In cosmology, dark energy creates a very small yet cosmically significant amount of negative pressure, which accelerates the expansion of the universe.

Stagnation pressure[edit]

Stagnation pressure is the pressure a fluid exerts when it is forced to stop moving. Consequently, although a fluid moving at higher speed will have a lower static pressure, it may have a higher stagnation pressure when forced to a standstill. Static pressure and stagnation pressure are related by:

where

is the stagnation pressure,

is the density,

is the flow velocity,

is the static pressure.

The pressure of a moving fluid can be measured using a Pitot tube, or one of its variations such as a Kiel probe or Cobra probe, connected to a manometer. Depending on where the inlet holes are located on the probe, it can measure static pressures or stagnation pressures.

Surface pressure and surface tension[edit]

There is a two-dimensional analog of pressure – the lateral force per unit length applied on a line perpendicular to the force.

Surface pressure is denoted by π:

and shares many similar properties with three-dimensional pressure. Properties of surface chemicals can be investigated by measuring pressure/area isotherms, as the two-dimensional analog of Boyle’s law, πA = k, at constant temperature.

Surface tension is another example of surface pressure, but with a reversed sign, because «tension» is the opposite to «pressure».

Pressure of an ideal gas[edit]

In an ideal gas, molecules have no volume and do not interact. According to the ideal gas law, pressure varies linearly with temperature and quantity, and inversely with volume:

where:

p is the absolute pressure of the gas,

n is the amount of substance,

T is the absolute temperature,

V is the volume,

R is the ideal gas constant.

Real gases exhibit a more complex dependence on the variables of state.^[18]

Vapour pressure[edit]

Vapour pressure is the pressure of a vapour in thermodynamic equilibrium with its condensed phases in a closed system. All liquids and solids have a tendency to evaporate into a gaseous form, and all gases have a tendency to condense back to their liquid or solid form.

The atmospheric pressure boiling point of a liquid (also known as the normal boiling point) is the temperature at which the vapor pressure equals the ambient atmospheric pressure. With any incremental increase in that temperature, the vapor pressure becomes sufficient to overcome atmospheric pressure and lift the liquid to form vapour bubbles inside the bulk of the substance. Bubble formation deeper in the liquid requires a higher pressure, and therefore higher temperature, because the fluid pressure increases above the atmospheric pressure as the depth increases.

The vapor pressure that a single component in a mixture contributes to the total pressure in the system is called partial vapor pressure.

Liquid pressure[edit]

When a person swims under the water, water pressure is felt acting on the person’s eardrums. The deeper that person swims, the greater the pressure. The pressure felt is due to the weight of the water above the person. As someone swims deeper, there is more water above the person and therefore greater pressure. The pressure a liquid exerts depends on its depth.

Liquid pressure also depends on the density of the liquid. If someone was submerged in a liquid more dense than water, the pressure would be correspondingly greater. Thus, we can say that the depth, density and liquid pressure are directly proportionate. The pressure due to a liquid in liquid columns of constant density or at a depth within a substance is represented by the following formula:

where:

p is liquid pressure,

g is gravity at the surface of overlaying material,

ρ is density of liquid,

h is height of liquid column or depth within a substance.

Another way of saying the same formula is the following:

Derivation of this equation

This is derived from the definitions of pressure and weight density. Consider an area at the bottom of a vessel of liquid. The weight of the column of liquid directly above this area produces pressure. From the definition we can express this weight of liquid as where the volume of the column is simply the area multiplied by the depth. Then we have With the «area» in the numerator and the «area» in the denominator canceling each other out, we are left with Written with symbols, this is our original equation:

The pressure a liquid exerts against the sides and bottom of a container depends on the density and the depth of the liquid. If atmospheric pressure is neglected, liquid pressure against the bottom is twice as great at twice the depth; at three times the depth, the liquid pressure is threefold; etc. Or, if the liquid is two or three times as dense, the liquid pressure is correspondingly two or three times as great for any given depth. Liquids are practically incompressible – that is, their volume can hardly be changed by pressure (water volume decreases by only 50 millionths of its original volume for each atmospheric increase in pressure). Thus, except for small changes produced by temperature, the density of a particular liquid is practically the same at all depths.

Atmospheric pressure pressing on the surface of a liquid must be taken into account when trying to discover the total pressure acting on a liquid. The total pressure of a liquid, then, is ρgh plus the pressure of the atmosphere. When this distinction is important, the term total pressure is used. Otherwise, discussions of liquid pressure refer to pressure without regard to the normally ever-present atmospheric pressure.

The pressure does not depend on the amount of liquid present. Volume is not the important factor – depth is. The average water pressure acting against a dam depends on the average depth of the water and not on the volume of water held back. For example, a wide but shallow lake with a depth of 3 m (10 ft) exerts only half the average pressure that a small 6 m (20 ft) deep pond does. (The total force applied to the longer dam will be greater, due to the greater total surface area for the pressure to act upon. But for a given 5-foot (1.5 m)-wide section of each dam, the 10 ft (3.0 m) deep water will apply one quarter the force of 20 ft (6.1 m) deep water). A person will feel the same pressure whether their head is dunked a metre beneath the surface of the water in a small pool or to the same depth in the middle of a large lake. If four vases contain different amounts of water but are all filled to equal depths, then a fish with its head dunked a few centimetres under the surface will be acted on by water pressure that is the same in any of the vases. If the fish swims a few centimetres deeper, the pressure on the fish will increase with depth and be the same no matter which vase the fish is in. If the fish swims to the bottom, the pressure will be greater, but it makes no difference what vase it is in. All vases are filled to equal depths, so the water pressure is the same at the bottom of each vase, regardless of its shape or volume. If water pressure at the bottom of a vase were greater than water pressure at the bottom of a neighboring vase, the greater pressure would force water sideways and then up the narrower vase to a higher level until the pressures at the bottom were equalized. Pressure is depth dependent, not volume dependent, so there is a reason that water seeks its own level.

Restating this as energy equation, the energy per unit volume in an ideal, incompressible liquid is constant throughout its vessel. At the surface, gravitational potential energy is large but liquid pressure energy is low. At the bottom of the vessel, all the gravitational potential energy is converted to pressure energy. The sum of pressure energy and gravitational potential energy per unit volume is constant throughout the volume of the fluid and the two energy components change linearly with the depth.^[19] Mathematically, it is described by Bernoulli’s equation, where velocity head is zero and comparisons per unit volume in the vessel are

Terms have the same meaning as in section Fluid pressure.

Direction of liquid pressure[edit]

An experimentally determined fact about liquid pressure is that it is exerted equally in all directions.^[20] If someone is submerged in water, no matter which way that person tilts their head, the person will feel the same amount of water pressure on their ears. Because a liquid can flow, this pressure isn’t only downward. Pressure is seen acting sideways when water spurts sideways from a leak in the side of an upright can. Pressure also acts upward, as demonstrated when someone tries to push a beach ball beneath the surface of the water. The bottom of a boat is pushed upward by water pressure (buoyancy).

When a liquid presses against a surface, there is a net force that is perpendicular to the surface. Although pressure doesn’t have a specific direction, force does. A submerged triangular block has water forced against each point from many directions, but components of the force that are not perpendicular to the surface cancel each other out, leaving only a net perpendicular point.^[20] This is why water spurting from a hole in a bucket initially exits the bucket in a direction at right angles to the surface of the bucket in which the hole is located. Then it curves downward due to gravity. If there are three holes in a bucket (top, bottom, and middle), then the force vectors perpendicular to the inner container surface will increase with increasing depth – that is, a greater pressure at the bottom makes it so that the bottom hole will shoot water out the farthest. The force exerted by a fluid on a smooth surface is always at right angles to the surface. The speed of liquid out of the hole is , where h is the depth below the free surface.^[20] This is the same speed the water (or anything else) would have if freely falling the same vertical distance h.

Kinematic pressure[edit]

is the kinematic pressure, where is the pressure and constant mass density. The SI unit of P is m²/s². Kinematic pressure is used in the same manner as kinematic viscosity in order to compute the Navier–Stokes equation without explicitly showing the density .

Navier–Stokes equation with kinematic quantities

See also[edit]

Notes[edit]

References[edit]

External links[edit]

• Introduction to Fluid Statics and Dynamics on Project PHYSNET
• Pressure being a scalar quantity
• wikiUnits.org — Convert units of pressure

This article is about pressure in the physical sciences. For other uses, see Pressure (disambiguation).

Pressure
Common symbols	p, P
SI unit	pascal [Pa]
In SI base units	1 N/m2, 1 kg/(m·s2), or 1 J/m3
Derivations from other quantities	p = F / A
Dimension	M L−1 T−2

Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.^[1]: 445 Gauge pressure (also spelled gage pressure)^[a] is the pressure relative to the ambient pressure.

Various units are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the SI unit of pressure, the pascal (Pa), for example, is one newton per square metre (N/m²); similarly, the pound-force per square inch (psi, symbol lbf/in²) is the traditional unit of pressure in the imperial and U.S. customary systems. Pressure may also be expressed in terms of standard atmospheric pressure; the atmosphere (atm) is equal to this pressure, and the torr is defined as 1⁄760 of this. Manometric units such as the centimetre of water, millimetre of mercury, and inch of mercury are used to express pressures in terms of the height of column of a particular fluid in a manometer.

Definition[edit]

Pressure is the amount of force applied perpendicular to the surface of an object per unit area. The symbol for it is «p» or P.^[2]
The IUPAC recommendation for pressure is a lower-case p.^[3]
However, upper-case P is widely used. The usage of P vs p depends upon the field in which one is working, on the nearby presence of other symbols for quantities such as power and momentum, and on writing style.

Formula[edit]

Mathematically:

^[4]

where:

is the pressure,

is the magnitude of the normal force,

is the area of the surface on contact.

Pressure is a scalar quantity. It relates the vector area element (a vector normal to the surface) with the normal force acting on it. The pressure is the scalar proportionality constant that relates the two normal vectors:

The minus sign comes from the convention that the force is considered towards the surface element, while the normal vector points outward. The equation has meaning in that, for any surface S in contact with the fluid, the total force exerted by the fluid on that surface is the surface integral over S of the right-hand side of the above equation.

It is incorrect (although rather usual) to say «the pressure is directed in such or such direction». The pressure, as a scalar, has no direction. The force given by the previous relationship to the quantity has a direction, but the pressure does not. If we change the orientation of the surface element, the direction of the normal force changes accordingly, but the pressure remains the same.^{[citation needed]}

Pressure is distributed to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. It is a fundamental parameter in thermodynamics, and it is conjugate to volume.^[5]

Units[edit]

The SI unit for pressure is the pascal (Pa), equal to one newton per square metre (N/m², or kg·m⁻¹·s⁻²). This name for the unit was added in 1971;^[6] before that, pressure in SI was expressed simply in newtons per square metre.

Other units of pressure, such as pounds per square inch (lbf/in²) and bar, are also in common use. The CGS unit of pressure is the barye (Ba), equal to 1 dyn·cm⁻², or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre (g/cm² or kg/cm²) and the like without properly identifying the force units. But using the names kilogram, gram, kilogram-force, or gram-force (or their symbols) as units of force is expressly forbidden in SI. The technical atmosphere (symbol: at) is 1 kgf/cm² (98.0665 kPa, or 14.223 psi).

Pressure is related to energy density and may be expressed in units such as joules per cubic metre (J/m³, which is equal to Pa).
Mathematically:

Some meteorologists prefer the hectopascal (hPa) for atmospheric air pressure, which is equivalent to the older unit millibar (mbar). Similar pressures are given in kilopascals (kPa) in most other fields, except aviation where the hecto- prefix is commonly used. The inch of mercury is still used in the United States. Oceanographers usually measure underwater pressure in decibars (dbar) because pressure in the ocean increases by approximately one decibar per metre depth.

The standard atmosphere (atm) is an established constant. It is approximately equal to typical air pressure at Earth mean sea level and is defined as 101325 Pa.

Because pressure is commonly measured by its ability to displace a column of liquid in a manometer, pressures are often expressed as a depth of a particular fluid (e.g., centimetres of water, millimetres of mercury or inches of mercury). The most common choices are mercury (Hg) and water; water is nontoxic and readily available, while mercury’s high density allows a shorter column (and so a smaller manometer) to be used to measure a given pressure. The pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation p = ρgh, where g is the gravitational acceleration. Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column does not define pressure precisely. When millimetres of mercury (or inches of mercury) are quoted today, these units are not based on a physical column of mercury; rather, they have been given precise definitions that can be expressed in terms of SI units.^[7] One millimetre of mercury is approximately equal to one torr. The water-based units still depend on the density of water, a measured, rather than defined, quantity. These manometric units are still encountered in many fields. Blood pressure is measured in millimetres of mercury in most of the world, and lung pressures in centimetres of water are still common.^{[citation needed]}

Underwater divers use the metre sea water (msw or MSW) and foot sea water (fsw or FSW) units of pressure, and these are the standard units for pressure gauges used to measure pressure exposure in diving chambers and personal decompression computers. A msw is defined as 0.1 bar (= 100000 Pa = 10000 Pa), is not the same as a linear metre of depth. 33.066 fsw = 1 atm^{[citation needed]} (1 atm = 101325 Pa / 33.066 = 3064.326 Pa). Note that the pressure conversion from msw to fsw is different from the length conversion: 10 msw = 32.6336 fsw, while 10 m = 32.8083 ft.^{[citation needed]}

Gauge pressure is often given in units with «g» appended, e.g. «kPag», «barg» or «psig», and units for measurements of absolute pressure are sometimes given a suffix of «a», to avoid confusion, for example «kPaa», «psia». However, the US National Institute of Standards and Technology recommends that, to avoid confusion, any modifiers be instead applied to the quantity being measured rather than the unit of measure.^[8] For example, «p_g = 100 psi» rather than «p = 100 psig».

Differential pressure is expressed in units with «d» appended; this type of measurement is useful when considering sealing performance or whether a valve will open or close.

Presently or formerly popular pressure units include the following:

• atmosphere (atm)
• manometric units:
  • centimetre, inch, millimetre (torr) and micrometre (mTorr, micron) of mercury,
  • height of equivalent column of water, including millimetre (mm H
    ₂O), centimetre (cm H
    ₂O), metre, inch, and foot of water;
• imperial and customary units:
  • kip, short ton-force, long ton-force, pound-force, ounce-force, and poundal per square inch,
  • short ton-force and long ton-force per square inch,
  • fsw (feet sea water) used in underwater diving, particularly in connection with diving pressure exposure and decompression;
• non-SI metric units:
  • bar, decibar, millibar,
    • msw (metres sea water), used in underwater diving, particularly in connection with diving pressure exposure and decompression,
  • kilogram-force, or kilopond, per square centimetre (technical atmosphere),
  • gram-force and tonne-force (metric ton-force) per square centimetre,
  • barye (dyne per square centimetre),
  • kilogram-force and tonne-force per square metre,
  • sthene per square metre (pieze).

Examples[edit]

As an example of varying pressures, a finger can be pressed against a wall without making any lasting impression; however, the same finger pushing a thumbtack can easily damage the wall. Although the force applied to the surface is the same, the thumbtack applies more pressure because the point concentrates that force into a smaller area. Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. Unlike stress, pressure is defined as a scalar quantity. The negative gradient of pressure is called the force density.^[9]

Another example is a knife. If we try to cut with the flat edge, force is distributed over a larger surface area resulting in less pressure, and it will not cut. Whereas using the sharp edge, which has less surface area, results in greater pressure, and so the knife cuts smoothly. This is one example of a practical application of pressure^[10]

For gases, pressure is sometimes measured not as an absolute pressure, but relative to atmospheric pressure; such measurements are called gauge pressure. An example of this is the air pressure in an automobile tire, which might be said to be «220 kPa (32 psi)», but is actually 220 kPa (32 psi) above atmospheric pressure. Since atmospheric pressure at sea level is about 100 kPa (14.7 psi), the absolute pressure in the tire is therefore about 320 kPa (46 psi). In technical work, this is written «a gauge pressure of 220 kPa (32 psi)». Where space is limited, such as on pressure gauges, name plates, graph labels, and table headings, the use of a modifier in parentheses, such as «kPa (gauge)» or «kPa (absolute)», is permitted. In non-SI technical work, a gauge pressure of 32 psi (220 kPa) is sometimes written as «32 psig», and an absolute pressure as «32 psia», though the other methods explained above that avoid attaching characters to the unit of pressure are preferred.^[8]

Gauge pressure is the relevant measure of pressure wherever one is interested in the stress on storage vessels and the plumbing components of fluidics systems. However, whenever equation-of-state properties, such as densities or changes in densities, must be calculated, pressures must be expressed in terms of their absolute values. For instance, if the atmospheric pressure is 100 kPa (15 psi), a gas (such as helium) at 200 kPa (29 psi) (gauge) (300 kPa or 44 psi [absolute]) is 50% denser than the same gas at 100 kPa (15 psi) (gauge) (200 kPa or 29 psi [absolute]). Focusing on gauge values, one might erroneously conclude the first sample had twice the density of the second one.^{[citation needed]}

Scalar nature[edit]

In a static gas, the gas as a whole does not appear to move. The individual molecules of the gas, however, are in constant random motion. Because we are dealing with an extremely large number of molecules and because the motion of the individual molecules is random in every direction, we do not detect any motion. When the gas is at least partially confined (that is, not free to expand rapidly), the gas will exhibit a static pressure. This confinement can be achieved with either a physical container of some sort, or in a gravitational well such as a planet, otherwise known as atmospheric pressure. In a physical container, the pressure of the gas originates from the molecules colliding with the walls of the container. We can put the walls of our container anywhere inside the gas, and the force per unit area (the pressure) is the same. We can shrink the size of our «container» down to a very small point (becoming less true as we approach the atomic scale), and the pressure will still have a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has magnitude but no direction sense associated with it. Pressure force acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular (at right angle) to the surface.^{[citation needed]}

A closely related quantity is the stress tensor σ, which relates the vector force to the
vector area via the linear relation .

This tensor may be expressed as the sum of the viscous stress tensor minus the hydrostatic pressure. The negative of the stress tensor is sometimes called the pressure tensor, but in the following, the term «pressure» will refer only to the scalar pressure.^{[citation needed]}

According to the theory of general relativity, pressure increases the strength of a gravitational field (see stress–energy tensor) and so adds to the mass-energy cause of gravity. This effect is unnoticeable at everyday pressures but is significant in neutron stars, although it has not been experimentally tested.^[11]

Types[edit]

Fluid pressure[edit]

Fluid pressure is most often the compressive stress at some point within a fluid. (The term fluid refers to both liquids and gases – for more information specifically about liquid pressure, see section below.)

Fluid pressure occurs in one of two situations:

1. An open condition, called «open channel flow», e.g. the ocean, a swimming pool, or the atmosphere.
2. A closed condition, called «closed conduit», e.g. a water line or gas line.

Pressure in open conditions usually can be approximated as the pressure in «static» or non-moving conditions (even in the ocean where there are waves and currents), because the motions create only negligible changes in the pressure. Such conditions conform with principles of fluid statics. The pressure at any given point of a non-moving (static) fluid is called the hydrostatic pressure.

Closed bodies of fluid are either «static», when the fluid is not moving, or «dynamic», when the fluid can move as in either a pipe or by compressing an air gap in a closed container. The pressure in closed conditions conforms with the principles of fluid dynamics.

The concepts of fluid pressure are predominantly attributed to the discoveries of Blaise Pascal and Daniel Bernoulli. Bernoulli’s equation can be used in almost any situation to determine the pressure at any point in a fluid. The equation makes some assumptions about the fluid, such as the fluid being ideal^[12] and incompressible.^[12] An ideal fluid is a fluid in which there is no friction, it is inviscid^[12] (zero viscosity).^[12] The equation for all points of a system filled with a constant-density fluid is^[13]

where:

p, pressure of the fluid,

= ρg, density × acceleration of gravity is the (volume-) specific weight of the fluid,^[12]

v, velocity of the fluid,

g, acceleration of gravity,

z, elevation,

, pressure head,

, velocity head.

Applications[edit]

• Hydraulic brakes
• Artesian well
• Blood pressure
• Hydraulic head
• Plant cell turgidity
• Pythagorean cup
• Pressure washing

Explosion or deflagration pressures[edit]

Explosion or deflagration pressures are the result of the ignition of explosive gases, mists, dust/air suspensions, in unconfined and confined spaces.

Negative pressures[edit]

While pressures are, in general, positive, there are several situations in which negative pressures may be encountered:

• When dealing in relative (gauge) pressures. For instance, an absolute pressure of 80 kPa may be described as a gauge pressure of −21 kPa (i.e., 21 kPa below an atmospheric pressure of 101 kPa). For example, abdominal decompression is an obstetric procedure during which negative gauge pressure is applied intermittently to a pregnant woman’s abdomen.
• Negative absolute pressures are possible. They are effectively tension, and both bulk solids and bulk liquids can be put under negative absolute pressure by pulling on them.^[14] Microscopically, the molecules in solids and liquids have attractive interactions that overpower the thermal kinetic energy, so some tension can be sustained. Thermodynamically, however, a bulk material under negative pressure is in a metastable state, and it is especially fragile in the case of liquids where the negative pressure state is similar to superheating and is easily susceptible to cavitation.^[15] In certain situations, the cavitation can be avoided and negative pressures sustained indefinitely,^[15] for example, liquid mercury has been observed to sustain up to −425 atm in clean glass containers.^[16] Negative liquid pressures are thought to be involved in the ascent of sap in plants taller than 10 m (the atmospheric pressure head of water).^[17]
• The Casimir effect can create a small attractive force due to interactions with vacuum energy; this force is sometimes termed «vacuum pressure» (not to be confused with the negative gauge pressure of a vacuum).
• For non-isotropic stresses in rigid bodies, depending on how the orientation of a surface is chosen, the same distribution of forces may have a component of positive pressure along one surface normal, with a component of negative pressure acting along another surface normal.
  • The stresses in an electromagnetic field are generally non-isotropic, with the pressure normal to one surface element (the normal stress) being negative, and positive for surface elements perpendicular to this.
• In cosmology, dark energy creates a very small yet cosmically significant amount of negative pressure, which accelerates the expansion of the universe.

Stagnation pressure[edit]

Stagnation pressure is the pressure a fluid exerts when it is forced to stop moving. Consequently, although a fluid moving at higher speed will have a lower static pressure, it may have a higher stagnation pressure when forced to a standstill. Static pressure and stagnation pressure are related by:

where

is the stagnation pressure,

is the density,

is the flow velocity,

is the static pressure.

The pressure of a moving fluid can be measured using a Pitot tube, or one of its variations such as a Kiel probe or Cobra probe, connected to a manometer. Depending on where the inlet holes are located on the probe, it can measure static pressures or stagnation pressures.

Surface pressure and surface tension[edit]

There is a two-dimensional analog of pressure – the lateral force per unit length applied on a line perpendicular to the force.

Surface pressure is denoted by π:

and shares many similar properties with three-dimensional pressure. Properties of surface chemicals can be investigated by measuring pressure/area isotherms, as the two-dimensional analog of Boyle’s law, πA = k, at constant temperature.

Surface tension is another example of surface pressure, but with a reversed sign, because «tension» is the opposite to «pressure».

Pressure of an ideal gas[edit]

In an ideal gas, molecules have no volume and do not interact. According to the ideal gas law, pressure varies linearly with temperature and quantity, and inversely with volume:

where:

p is the absolute pressure of the gas,

n is the amount of substance,

T is the absolute temperature,

V is the volume,

R is the ideal gas constant.

Real gases exhibit a more complex dependence on the variables of state.^[18]

Vapour pressure[edit]

Vapour pressure is the pressure of a vapour in thermodynamic equilibrium with its condensed phases in a closed system. All liquids and solids have a tendency to evaporate into a gaseous form, and all gases have a tendency to condense back to their liquid or solid form.

The atmospheric pressure boiling point of a liquid (also known as the normal boiling point) is the temperature at which the vapor pressure equals the ambient atmospheric pressure. With any incremental increase in that temperature, the vapor pressure becomes sufficient to overcome atmospheric pressure and lift the liquid to form vapour bubbles inside the bulk of the substance. Bubble formation deeper in the liquid requires a higher pressure, and therefore higher temperature, because the fluid pressure increases above the atmospheric pressure as the depth increases.

The vapor pressure that a single component in a mixture contributes to the total pressure in the system is called partial vapor pressure.

Liquid pressure[edit]

When a person swims under the water, water pressure is felt acting on the person’s eardrums. The deeper that person swims, the greater the pressure. The pressure felt is due to the weight of the water above the person. As someone swims deeper, there is more water above the person and therefore greater pressure. The pressure a liquid exerts depends on its depth.

Liquid pressure also depends on the density of the liquid. If someone was submerged in a liquid more dense than water, the pressure would be correspondingly greater. Thus, we can say that the depth, density and liquid pressure are directly proportionate. The pressure due to a liquid in liquid columns of constant density or at a depth within a substance is represented by the following formula:

where:

p is liquid pressure,

g is gravity at the surface of overlaying material,

ρ is density of liquid,

h is height of liquid column or depth within a substance.

Another way of saying the same formula is the following:

Derivation of this equation

This is derived from the definitions of pressure and weight density. Consider an area at the bottom of a vessel of liquid. The weight of the column of liquid directly above this area produces pressure. From the definition we can express this weight of liquid as where the volume of the column is simply the area multiplied by the depth. Then we have With the «area» in the numerator and the «area» in the denominator canceling each other out, we are left with Written with symbols, this is our original equation:

The pressure a liquid exerts against the sides and bottom of a container depends on the density and the depth of the liquid. If atmospheric pressure is neglected, liquid pressure against the bottom is twice as great at twice the depth; at three times the depth, the liquid pressure is threefold; etc. Or, if the liquid is two or three times as dense, the liquid pressure is correspondingly two or three times as great for any given depth. Liquids are practically incompressible – that is, their volume can hardly be changed by pressure (water volume decreases by only 50 millionths of its original volume for each atmospheric increase in pressure). Thus, except for small changes produced by temperature, the density of a particular liquid is practically the same at all depths.

Atmospheric pressure pressing on the surface of a liquid must be taken into account when trying to discover the total pressure acting on a liquid. The total pressure of a liquid, then, is ρgh plus the pressure of the atmosphere. When this distinction is important, the term total pressure is used. Otherwise, discussions of liquid pressure refer to pressure without regard to the normally ever-present atmospheric pressure.

The pressure does not depend on the amount of liquid present. Volume is not the important factor – depth is. The average water pressure acting against a dam depends on the average depth of the water and not on the volume of water held back. For example, a wide but shallow lake with a depth of 3 m (10 ft) exerts only half the average pressure that a small 6 m (20 ft) deep pond does. (The total force applied to the longer dam will be greater, due to the greater total surface area for the pressure to act upon. But for a given 5-foot (1.5 m)-wide section of each dam, the 10 ft (3.0 m) deep water will apply one quarter the force of 20 ft (6.1 m) deep water). A person will feel the same pressure whether their head is dunked a metre beneath the surface of the water in a small pool or to the same depth in the middle of a large lake. If four vases contain different amounts of water but are all filled to equal depths, then a fish with its head dunked a few centimetres under the surface will be acted on by water pressure that is the same in any of the vases. If the fish swims a few centimetres deeper, the pressure on the fish will increase with depth and be the same no matter which vase the fish is in. If the fish swims to the bottom, the pressure will be greater, but it makes no difference what vase it is in. All vases are filled to equal depths, so the water pressure is the same at the bottom of each vase, regardless of its shape or volume. If water pressure at the bottom of a vase were greater than water pressure at the bottom of a neighboring vase, the greater pressure would force water sideways and then up the narrower vase to a higher level until the pressures at the bottom were equalized. Pressure is depth dependent, not volume dependent, so there is a reason that water seeks its own level.

Restating this as energy equation, the energy per unit volume in an ideal, incompressible liquid is constant throughout its vessel. At the surface, gravitational potential energy is large but liquid pressure energy is low. At the bottom of the vessel, all the gravitational potential energy is converted to pressure energy. The sum of pressure energy and gravitational potential energy per unit volume is constant throughout the volume of the fluid and the two energy components change linearly with the depth.^[19] Mathematically, it is described by Bernoulli’s equation, where velocity head is zero and comparisons per unit volume in the vessel are

Terms have the same meaning as in section Fluid pressure.

Direction of liquid pressure[edit]

An experimentally determined fact about liquid pressure is that it is exerted equally in all directions.^[20] If someone is submerged in water, no matter which way that person tilts their head, the person will feel the same amount of water pressure on their ears. Because a liquid can flow, this pressure isn’t only downward. Pressure is seen acting sideways when water spurts sideways from a leak in the side of an upright can. Pressure also acts upward, as demonstrated when someone tries to push a beach ball beneath the surface of the water. The bottom of a boat is pushed upward by water pressure (buoyancy).

When a liquid presses against a surface, there is a net force that is perpendicular to the surface. Although pressure doesn’t have a specific direction, force does. A submerged triangular block has water forced against each point from many directions, but components of the force that are not perpendicular to the surface cancel each other out, leaving only a net perpendicular point.^[20] This is why water spurting from a hole in a bucket initially exits the bucket in a direction at right angles to the surface of the bucket in which the hole is located. Then it curves downward due to gravity. If there are three holes in a bucket (top, bottom, and middle), then the force vectors perpendicular to the inner container surface will increase with increasing depth – that is, a greater pressure at the bottom makes it so that the bottom hole will shoot water out the farthest. The force exerted by a fluid on a smooth surface is always at right angles to the surface. The speed of liquid out of the hole is , where h is the depth below the free surface.^[20] This is the same speed the water (or anything else) would have if freely falling the same vertical distance h.

Kinematic pressure[edit]

is the kinematic pressure, where is the pressure and constant mass density. The SI unit of P is m²/s². Kinematic pressure is used in the same manner as kinematic viscosity in order to compute the Navier–Stokes equation without explicitly showing the density .

Navier–Stokes equation with kinematic quantities

See also[edit]

Notes[edit]

References[edit]

External links[edit]

• Introduction to Fluid Statics and Dynamics on Project PHYSNET
• Pressure being a scalar quantity
• wikiUnits.org — Convert units of pressure