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 $g = 10 \ m/s^2$)

$A$ barometer tube,containing mercury,is lowered in a vessel containing mercury until only $50 \, cm$ of the tube is above the level of mercury in the vessel. If the atmospheric pressure is $75 \, cm$ of mercury,what is the pressure at the top of the tube?

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,$\rho = 1.06 \times 10^{3} \; kg \; m^{-3}$,$g = 9.8 \; m \; s^{-2}$)

The atmospheric pressure and height of the barometer column are $10^5 \, Pa$ and $760 \, mm$ respectively on the Earth's surface. If the barometer is taken to the Moon,then the column height will be ........ $mm$.

$A$ 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 $= 10 \, m/s^2$).

Explain how an open-ended tube manometer measures pressure.