Physics · Mechanical Properties Of Fluids · NEET
A point deep in the liquid has to support the entire column of liquid sitting on top of it. More liquid above means more weight pressing down, so the pressure is larger. That is why the pressure at the bottom of a tank is more than near the top.
Take a small cylinder of liquid, base area A and height h, at rest. Vertical forces must balance. Downward force at top = P1 x A. Upward force at bottom = P2 x A. Weight of the cylinder = m x g pulling down. Balance gives (P2 - P1)A = mg. The mass is m = rho x V = rho x A x h. Substitute: (P2 - P1)A = rho A h g. Cancel A on both sides: P2 - P1 = rho g h.
Both the pressure forces (P x A) and the weight (rho x A x h x g) contain the same area A, so when you divide the whole equation by A, it disappears. This is the key result: the pressure difference does not depend on the area or the shape of the container, only on the vertical depth h, the density rho and g.
rho g h is only the extra pressure added by a depth h of liquid (the gauge pressure). If the top surface is open to air, you must also add the atmospheric pressure P0 pressing on the surface. So the total (absolute) pressure at depth h is P = P0 + rho g h.
No. Two tanks, one narrow and one very wide, filled to the same depth of the same liquid, have exactly the same pressure at the bottom. Pressure depends only on the vertical depth, not on the total volume or width. This surprises many students and is a common NTA trick.
A submarine is designed to withstand an absolute pressure of 100 atm. How deep can it go below the water surface? (density of water = 1000 kg per m cubed, 1 atm = 1 x 10^5 Pa, g = 10 m per s squared)
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Yes. For a liquid of constant density, P = P0 + rho g h is a straight-line (linear) relation. Every extra metre of depth adds the same amount of pressure, rho g per metre.
rho is the mass density of the fluid, in kg per cubic metre. For water it is about 1000 kg per m cubed. A denser liquid like mercury (13600 kg per m cubed) gives much more pressure for the same depth.
rho g h alone is the gauge pressure - the pressure added by the liquid column only. Absolute pressure includes the atmosphere on top: P = P0 + rho g h.
In the derivation, only vertical depth h matters. Two points at the same depth have the same h, so they have the same pressure, as long as they are in the same connected fluid at rest.
Yes. We take rho as constant, which is true for liquids. For a gas, rho changes with height, so pressure does not follow a simple rho g h law over large heights.
