# Fluid Mechanics/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.

## Static Pressure

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

Static Pressure or simply 'pressure' is the force per unit area applied in the direction perpendicular to a surface. It has to be noted that this definition is only applicable to static fluids (dynamic pressure for fluid in motion).The idea of pressure is as 'stress' in solid mechanics. Mathematically, pressure is defined as

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

where:

P is Static 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

### Absolute pressure and gauge pressure

==Mass Density ==It is the ratio of mass per unit volume. It is denoted by symbol rho ρ=mass/volume. And it’s S.I. unit is kg/m3