$A$ submarine is designed to withstand an absolute pressure of $100 \text{ atm}$. How deep can it go below the water surface (in $\text{ m}$)? (Consider the density of water = $1000 \text{ kg/m}^3$, $1 \text{ atm} = 1 \times 10^5 \text{ Pa}$, and gravitational acceleration $g = 10 \text{ m/s}^2$)

Discuss the variation of pressure with depth or pressure produced due to fluid depth $h$ and density of fluid $\rho$.

At what speed,the velocity head of water is equal to the pressure head of $40 \, cm$ of mercury? (Given: Density of mercury = $13.6 \times 10^3 \, kg/m^3$,Density of water = $10^3 \, kg/m^3$,$g = 9.8 \, m/s^2$)

$A$ bubble of volume $V_0$ is released from a depth $h$ in a lake. If the atmospheric pressure is $P$ and the temperature is assumed to be constant,what is the new volume of the bubble when it reaches the surface? (Density of water is $\rho$)

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

What does it mean when the height of a barometer is falling?