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:

A horizontal pipe line carries water in a streamline flow. At a point along the pipe where cross-sectional area is 10 cm², the velocity of water is 1 m/s and pressure is 2000 Pa. The pressure of water at another point where cross-sectional area is 5 cm², is: (Density of water=1000 kg/m³)

1.  250 Pa

2.  500 Pa

3.  1000 Pa

4.  2000 Pa

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

In a horizontal pipe line the pressure falls by $16$ ${\mathrm{Nm}}^{-2}$ between two points separated by a distance of 2 km. Density of oil is $800$ $\mathrm{kg}$ ${\mathrm{m}}^{-3}$. Change in kinetic energy per kg of the oil flowing in the tube is:

1. $2\times {10}^3$ $\mathrm{J}/\mathrm{kg}$

2. $2\times {10}^2$ $\mathrm{J}/\mathrm{kg}$

3. $2\times {10}^{-2}$ $\mathrm{J}/\mathrm{kg}$

4. $2\times {10}^{-3}$ $\mathrm{J}/\mathrm{kg}$

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