$A$ pressure of $1 \,mm$ of mercury is equivalent to

$A$ barometer is kept in an elevator accelerating upwards with an acceleration $a$. Find the most likely pressure inside the elevator.

If the atmospheric pressure is $P_a$,then the pressure $P$ at depth $h$ below the surface of a liquid of density $\rho$ open to the atmosphere is:

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

$(a)$ Pressure decreases as one ascends the atmosphere. If the density of air is $\rho$,what is the change in pressure $dp$ over differential height $dh$?
$(b)$ Considering the pressure $P$ to be proportional to the density,find the pressure $P$ at a height $h$ if the pressure on the surface of the earth is $P_{0}$.
$(c)$ If $P_{0} = 1.03 \times 10^5 \text{ N/m}^2$,$\rho_0 = 1.29 \text{ kg/m}^3$,and $g = 9.8 \text{ m/s}^2$,at what height will the pressure drop to $\frac{1}{10}$ of the value at the surface of the earth?
$(d)$ This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.

Describe the mercury barometer for the measurement of atmospheric pressure.