# 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: mmHg). 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