Module 2: Fluid Statics
  Lecture 4: Basic equation: derivation, pressure variation in an incompressible fluid
 
Notes:
  1. Pressure gradient in a static fluid is zero if there is no gravity. Alternatively, the net force acting on a fluid volume is zero because pressure–force balances the force due to gravity. Alternatively, pressure-variation occurs in a static fluid because of gravity only.
  2. If the fluid is water, static pressure is often referred as ‘hydrostatic' pressure.  
  3. If a body is submerged in a fluid, which is in contact with (or open to) atmosphere, the atmospheric pressure acts uniformly on the body. For most of the engineering applications one is interested in calculating pressure due to the fluid only, ignoring the atmospheric pressure. In such case, the pressure is specified as a gauge pressure (above the atmosphere pressure): . Therefore, the gauge pressure may be negative if the pressure in the fluid is sub or below atmospheric. Absolute pressure is always positive
  4. Pressure in the atmosphere may vary, of course, over a relatively longer altitude, because the density of air is small (1 kg/m3 in comparison to 1000 kg/m3 for water).
    Consider an atmosphere consisting of ideal gases.
    Static pressure gradient

And,

 
Substituting,
(Fig. 4a)

or,

 

If or an isothermal atmosphere

And,

or,

The pressure varies (decreases) exponentially with altitude, if temperature variation is considered negligible.