The pressure at the bottom of a water tank is $4 P$,where $P$ is atmospheric pressure. If water is drawn out until the water level decreases by $\frac{3}{5}$ of its initial height,then the pressure at the bottom of the tank is .........

$A$ barometer is constructed using a liquid (density $= 760 \; kg/m^3$). What would be the height (in $m$) of the liquid column,when a mercury barometer reads $76 \; cm$? (density of mercury $= 13600 \; kg/m^3$)

$A$ liquid boils when its vapour pressure equals

During blood transfusion,the needle is inserted into a vein where the gauge pressure is $2000 \; Pa$. At what height (in $m$) must the blood container be placed so that blood may just enter the vein? (Density of whole blood,$\rho = 1.06 \times 10^{3} \; kg \; m^{-3}$,$g = 9.8 \; m \; s^{-2}$)

Consider the wall of a dam to be straight with height $H$ and length $L$. It holds a lake of water of height $h$ $(h < H)$ on one side. Let the density of water be $\rho_w$. Denote the torque about the axis along the bottom length of the wall by $\tau_1$. Denote also a similar torque due to the water up to height $h/2$ and wall length $L/2$ by $\tau_2$. Then $\tau_1 / \tau_2$ (ignore atmospheric pressure) is

Show that the pressure produced due to a fluid column depends on the height of the fluid column and the density of the fluid.