Water flows in a streamline motion through a horizontal pipe of circular cross-section. The pressure difference of water between $P$ and $Q$ is $15 \text{ Nm}^{-2}$. The area of cross-section at $P$ and $Q$ are $40 \text{ cm}^2$ and $20 \text{ cm}^2$, respectively. The rate of flow of water through the pipe, in $\text{cm}^3\text{s}^{-1}$, is : [Take density of water = $1000 \text{ kg m}^{-3}$]

$A$ train with cross-sectional area $S_t$ is moving with speed $v_t$ inside a long tunnel of cross-sectional area $S_0$ $(S_0 = 4S_t)$. Assume that almost all the air (density $\rho$) in front of the train flows back between its sides and the walls of the tunnel. Also,the air flow with respect to the train is steady and laminar. Take the ambient pressure and that inside the train to be $p_0$. If the pressure in the region between the sides of the train and the tunnel walls is $p$,then $p_0 - p = \frac{7}{2N} \rho v_t^2$. The value of $N$ is. . . . .

Explain blood flow and heart attack with the help of Bernoulli's principle.

The area of cross-section of a large tank is $0.5 \; m^{2}$. It has a narrow opening near the bottom having an area of cross-section $1 \; cm^{2}$. $A$ load of $25 \; kg$ is applied on the water at the top in the tank. Neglecting the speed of water in the tank,the velocity of the water coming out of the opening at the time when the height of water level in the tank is $40 \; cm$ above the bottom will be $\dots \; cm \; s^{-1}$. [Take $g = 10 \; m \; s^{-2}$]

If water is flowing in a pipe with speed $2 \, m/s$,then its kinetic energy per unit volume is ........... $J/m^3$.

$A$ large cylindrical tank of cross-sectional area $1\ m^2$ is filled with water. It has a small hole at a height of $1\ m$ from the bottom. $A$ movable piston of mass $5\ kg$ is fitted on the top of the tank such that it can slide in the tank freely without friction. $A$ load of $45\ kg$ is applied on the top of the water by the piston,as shown in the figure. The value of $v$ when the piston is $7\ m$ above the bottom is $(g = 10\ m/s^2)$ ....... $m/s$