Fluid Statics/Fundamentals of Fluid Statics

Hydrostatic Equilibrium

Hydrostatic equilibrium or hydrostatic balance is the defining condition of fluids studied in fluid statics. Hydrostatic equilibrium is the condition in which a volume of fluid is at rest or moves with constant velocity. Although individual molecules in a fluid are not at rest with respect to each other, hydrostatic equilibrium mandates that the system as a whole must be stationary in some inertial reference frame. In other words, a system in hydrostatic equilibrium contains fluid that is not accelerating.

Pressure

This figure shows pressure exerted by particle collisions inside a closed container. The collisions that exert the pressure are highlighted in red.

Pressure is the force per unit area applied in the direction perpendicular to a surface. Mathematically, pressure is defined as

$P = \frac{dF}{dA}$

where:

P is pressure

F is the component of force perpendicular to the surface

A is the area of the surface

When a force is constant over an area, the pressure acting on that area is simply

$P = \frac{F}{A}$

Pressure is a scalar quantity, thus it acts in all directions at any given point. In order for pressure to create a force, the pressure must be integrated over some area.

Units of pressure

In 1971, the SI unit for pressure became known as the pascal (symbol: Pa), equal to one newton per square meter (N/m² or kg·m⁻¹·s⁻²), in honor of the French physicist Blaise Pascal. Since the pascal is a relatively small amount of pressure for many engineering purposes, the kilopascal (1 kPa = 1,000 Pa) and the megapascal (1 MPa = 1,000,000 Pa) are often used in its place. The bar (symbol: bar) is defined as 100 kPa, or 100,000 Pa, which has the same order of magnitude as atmospheric pressure. However, atmospheric pressure is most closely equivalent to the standard atmosphere (symbol: atm), defined as 101,325 Pa.

The English unit for pressure is the pound per square inch (symbol: psi, lbf/in², or lbf/sq in). It is the pressure resulting from a force of one pound-force applied to an area of one square inch. 1 psi is approximately equal to 6894.757 Pa.

Another non-SI unit of pressure is the torr (Symbol: Torr), which is defined to be 760 atm. The torr was chosen to be approximately equal to the pressure exerted by one millimeter of mercury (symbol: mm_Hg). The torr was named in honor of Evangelista Torricelli, an Italian physicist who discovered the use of the mercury barometer in 1643.

What follows is a table listing the conversions between common units of pressure.

Pressure units

	pascal	bar	standard atmosphere	torr	pound per square inch
	Pa	bar	atm	Torr	psi
1 Pa	≡ 1 N/m2	10−5	9.8692×10−6	7.5006×10−3	145.04×10−6
1 bar	105	≡ 105 Pa	0.98692	750.06	14.5037744
1 at	0.980665 ×105	0.980665	0.96784	735.56	14.223
1 atm	1.01325 ×105	1.01325	≡ p0	760	14.696
1 Torr	133.322	1.3332×10−3	1.3158×10−3	≈ 1 mmHg	19.337×10−3
1 psi	6.895×103	68.948×10−3	68.046×10−3	51.715	≡ 1 lbf/in2