At what speed,the velocity head of water is equal to the pressure head of $40 \, cm$ of mercury? (Given: Density of mercury = $13.6 \times 10^3 \, kg/m^3$,Density of water = $10^3 \, kg/m^3$,$g = 9.8 \, m/s^2$)

If the pressure at half the depth of a lake is equal to $2/3$ of the pressure at the bottom of the lake,then what is the depth of the lake in $m$? (Assume atmospheric pressure $P_0 = 10^5 \ Pa$,density of water $\rho = 10^3 \ kg/m^3$,and $g = 10 \ m/s^2$)

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

$A$ manometer reads the pressure of a gas in an enclosure as shown in the figure. The absolute and gauge pressure of the gas in $cm$ of mercury are (Take atmospheric pressure $= 76\,cm$ of mercury)

$A$ submarine experiences a pressure of $5.05 \times 10^6 \, Pa$ at a depth of $d_1$ in a sea. When it goes further to a depth of $d_2,$ it experiences a pressure of $8.08 \times 10^6 \, Pa.$ Then $d_2 - d_1$ is approximately ........ $m$ (density of water $= 10^3 \, kg/m^3$ and acceleration due to gravity $= 10 \, m/s^2$).

Write the formula of pressure at depth $h$ in a liquid.