A large open tank with a square hole of side \(0.1\) cm in the wall at a depth of \(0.2\) m from the top is completely filled with a liquid. The rate of flow of liquid (in ${\mathrm{cm}}^3$/s) through the hole will be: 

A tank is filled with water up to a height \(\mathrm H.\) Water is allowed to come out of a hole \(\mathrm P\) in one of the walls at a depth \(\mathrm D\) below the surface of water. Express the horizontal distance \(\mathrm{x}\) in terms of \(\mathrm H\) and \(\mathrm {D}\text :\)
                    

1. $\mathrm{x}=\sqrt{\mathrm{D}(\mathrm{H}-\mathrm{D})}$

2. $\mathrm{x}=\sqrt{\frac{\mathrm{D}(\mathrm{H}-\mathrm{D})}{2}}$

3. $\mathrm{x}=2\sqrt{\mathrm{D}(\mathrm{H}-\mathrm{D})}$

4. $\mathrm{x}=4\sqrt{\mathrm{D}(\mathrm{H}-\mathrm{D})}$

The pressure of water in a water pipe when tap is opened and closed are respectively \(3\times10^5\) Nm^–2 and \(3.5\times10^5\) Nm^–2. With open tap, the velocity of water flowing is:
              
1. \(10\) ms^–1                           
2. \(5\) ms^–1
3. \(20\) ms^–1       
4. \(15\) ms^–1

The following fig. shows the flow of liquid through a horizontal pipe. Three tubes A, B and C are connected to the pipe. The radii of the tubes A, B and C at the junction are respectively 2 cm, 1 cm and 2 cm. It can be said that the:

There is an orifice at some depth in the water tank. Absolute pressure at the level of the orifice in the water tank is 4 atmospheric pressure. The density of water is ${10}^3$ $\mathrm{kg}/{\mathrm{m}}^3$ and 1 atm pressure = ${10}^5$ N/${\mathrm{m}}^2$. The speed of water coming out of the orifice is: 
1. 10 m/s
2. 20 m/s
3. 10$\sqrt{6}$ m/s
4. 10$\sqrt{2}$ m/s

The velocity of kerosene oil in a horizontal pipe is 5 m/s. If $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$, then the velocity head of oil will be:
1. 1.25 m
2. 12.5 m
3. 0.125 m                             
4. 125 m

A small hole of an area of cross-section \(2~\text{mm}^2\) is present near the bottom of a fully filled open tank of height \(2~\text{m}\). Taking \(g = 10~\text{m/s}^2\)${\mathrm{}}^{}$, the rate of flow of water through the open hole would be nearly:
1. \(6.4\times10^{-6}~\text{m}^{3}/\text{s}\)
2. \(12.6\times10^{-6}~\text{m}^{3}/\text{s}\)
3. \(8.9\times10^{-6}~\text{m}^{3}/\text{s}\)
4. \(2.23\times10^{-6}~\text{m}^{3}/\text{s}\)

The speed of flow past the lower surface of a wing of an aeroplane is 50 m/s. What speed of flow over the upper surface will give a dynamic lift of 1000 Pa? (Density of air = 1.3 kg/m³):
        
1. 25.55 m/s

2. 63.55 m/s

3. 13.25 m/s

4. 6.355 m/s

Water flows through a frictionless tube with a varying cross-section as shown in the figure. Variation of pressure P at point x along the axis is roughly given by:

1.		2.
3.		4.

An engine pumps water continuously through a hose. Water leaves the hose with a velocity \(v\) and \(m\) is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?
1. $\frac{1}{2}m{v}^3$                                   

2. $m{v}^3$

3. $\frac{1}{2}m{v}^2$                                   

4. $\frac{1}{2}{m}^2{v}^2$