Module 2: Fluid Statics
  Lecture 5: Pressure variation in two immiscible fluids, manometer, barometer
 
 
(2) Pressure- variation in two-immiscible liquids (one is heavier than the other)

(Fig. 5a)
 

Consider two liquids of densities . Depth (measured form the top) of the top-fluid is and that of the bottom-fluid is
Put the co-ordinate axis at the bottom (left). The governing equation for the static fluid is
 
or   

On integration,   
Similarly,   
or

One can get similar expression by putting the co-ordinate axis at the top of the surface, with z-axis pointing vertically downward (right):


or,   
On integration
Similarly,
or,

Note: Both expressions are same!