Consider a completely full cylindrical water tank of height $1.6 \ m$ and cross-sectional area $0.5 \ m^2$. It has a small hole in its side at a height $90 \ cm$ from the bottom. Assume the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load of $50 \ kg$ is applied at the top surface of the water in the tank,then the velocity of the water coming out at the instant when the hole is opened is ......... $m/s$ $(g=10 \ m/s^2)$.

The Pitot tube shown in the figure is used to measure fluid flow velocity in a pipe of cross-sectional area $S$. It was invented by a French engineer Henri Pitot in the early $18^{th}$ century. The volume of the gas flowing across the section of the pipe per unit time is (The difference in the liquid columns is $\Delta h$,$\rho_0$ and $\rho$ are the densities of liquid and the gas respectively):

$A$ horizontal pipe of non-uniform cross-section allows water to flow through it with a velocity $1 \ m/s$ when the pressure is $50 \ kPa$ at a point. If the velocity of flow has to be $2 \ m/s$ at some other point,the pressure at that point should be: (in $kPa$)

Write the limitations of Bernoulli's equation.

In a horizontal tube,the water pressure changes by $1500 \text{ N m}^{-2}$ between points $A$ and $B$ as shown in the figure below. The cross-sectional areas at $A$ and $B$ of the tube are $40 \text{ cm}^2$ and $20 \text{ cm}^2$,respectively. Find the rate of flow of water through the tube.

Consider a cylindrical tank of radius $1\,m$ filled with water. The top surface of the water is at $15\,m$ from the bottom of the cylinder. There is a hole on the wall of the cylinder at a height of $5\,m$ from the bottom. $A$ force of $5 \times 10^{5}\,N$ is applied on the top surface of the water using a piston. Calculate the speed of efflux from the hole. (Given: atmospheric pressure $P_{A} = 1.01 \times 10^{5}\,Pa$,density of water $\rho_{w} = 1000\,kg/m^{3}$,and gravitational acceleration $g = 10\,m/s^{2}$) (in $,m/s$)