By sucking through a straw,a student can reduce the pressure in his lungs to $750\, mm$ of $Hg$ (density $= 13.6\, g/cm^3$). Using the straw,he can drink water from a glass up to a maximum depth of ....... $cm$.

$A$ vertical off-shore structure is built to withstand a maximum stress of $10^9 \; Pa$. Is the structure suitable for putting up on top of an oil well in the ocean? Take the depth of the ocean to be roughly $3 \; km$,and ignore ocean currents.

What would be the absolute pressure at a depth of $1 \,km$ below the ocean surface? [Given: density of water $\rho = 10^{3} \,kg/m^{3}$,$g = 10 \,m/s^{2}$,$1 \,atm = 1.01 \times 10^{5} \,N/m^{2}$]

When an airplane flies at a higher altitude,it is not advisable to keep a fountain pen in one's pocket. Why?

$(a)$ 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.

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