Fluid Statics/Fundamentals of Fluid Statics
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 is the force per unit area applied in the direction perpendicular to a surface. Mathematically, pressure is defined as
- 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
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.
|pascal||bar||standard atmosphere||torr||pound per square inch|
|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|