Two immiscible liquids are filled in a conical flask as shown in the figure. The cross-sectional area is shown. $A$ small hole of area $a$ is made in the lower end of the cone. Find the speed of liquid flow from the hole.

At a hydroelectric power plant,the water pressure head is at a height of $300\; m$ and the water flow available is $100\; m^{3} s^{-1}.$ If the turbine generator efficiency is $60\%,$ estimate the electric power available from the plant (in $MW$) $\left(g=9.8\; m s^{-2}\right).$

As shown in the figure, a pump is designed as a horizontal cylinder with a piston having area $A$ and an outlet orifice having an area $a$. The piston moves with a constant velocity under the action of force $F$. If the density of the liquid is $\rho$, then the speed of the liquid emerging from the orifice is (assume $A \gg a$):

Water is flowing through a horizontal pipe in streamline flow. At the narrowest part of the pipe,

Consider the following equation of Bernoulli's theorem: $P + \frac{1}{2}\rho V^2 + \rho gh = K$ (constant). The dimensions of $K/P$ are the same as those of which of the following?

$A$ 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. . . . .