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

What are the difficulties arising from using water in a barometer instead of mercury?

$A$ healthy adult of height $1.7 \,m$ has an average blood pressure $(BP)$ of $100 \,mm$ of $Hg$. The heart is typically at a height of $1.3 \,m$ from the foot. Take the density of blood to be $10^3 \,kg/m^3$ and note that $100 \,mm$ of $Hg$ is equivalent to $13.3 \,kPa$ (kilo pascals). The ratio of $BP$ in the foot region to that in the head region is close to:

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

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

Mention two instruments which measure the atmospheric pressure.