The term 'fluid' is used for ............

$A$ cylindrical vessel of base radius $R$ and height $H$ has a narrow neck of height $h$ and radius $r$ at one end (see figure). The vessel is filled with water (density $\rho_w$) and its neck is filled with immiscible oil (density $\rho_0$). Then,the pressure at

$A$ bubble from the bottom of a lake rises to its surface. Its volume doubles in the process. Assuming isothermal conditions, atmospheric pressure $= 75 \, cm$ of $Hg$, and the ratio of the densities of mercury and water $= 40/3$. The depth of the lake will be ..... $m$.

Mountaineers suffer from nose bleeding (epistaxis) at higher altitudes. Explain.

$A$ person of height $1.65 \,m$ is standing upright. The additional external force required by a blood vessel of length $1 \,cm$, diameter $1 \,mm$ at the feet to balance the pressure compared to a similar blood vessel in the head is (Density of blood $= 1.1 \times 10^3 \,kg \,m^{-3}$, $g = 10 \,ms^{-2}$) (in $\,N$)

Two points $A$ and $B$ are at the same depth in a liquid at rest. Then the pressure on them $P_A$ ........... $P_B$.