Prove that in static equilibrium the pressure exerted by a fluid decre

1.	Prove that in static equilibrium the pressure exerted by a fluid decreases with its height.
Answer» Solution :Let us assume two layers at heights h and h + dh from the base inside a fluid. Let the density of the fluid = `rho`. A PART having UNIT cross-sectional area and THICKNESS dh is considered. So, the mass of the part = `rhodh`. Let the upward pressure on this part be p and the downward pressure = p + dp. `therefore` In EQUILIBRIUM, `(p+dp)-p+(rhodh*g)=0or,(dp)/(dh)=-rhog` `(dp)/(dh)` is negative, which indicates that with increase in h, the value of p decreases. So, it is seen that the pressure exerted by the fluid goes on DECREASING with its height from the base.

Discussion