Question

If fluid is at rest in a container of a narrow mouth at a certain column height and same fluid is at rest at same column height in a container having broad mouth, will the pressure be different at certain depth from fluid surface​

Answer 1

No, the pressure will not different at certain depth from fluid surface for the two different containers if fluid is rest at same column height.

Explanation:

• As per Hydrostatic law, if P is the pressure, $\rho$ is the density of the fluid, g is the acceleration due to gravity and h is the height of the fluid column, then

                                           $\boxed{\bold{P = \rho gh} }$       or     $\boxed{\bold{P \propto h}}$

• From the above equation of hydrostatic pressure we get to know that pressure is directly proportional to the height of the liquid, i.e. it does not depend on the shape of the container.
• The above two points shows that the pressure at certain depth from fluid surface of a narrow mouth container is same as container having broad mouth if fluid is rest at same column height.