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 \(H.\) The water is allowed to come out of a hole \(P\) in one of the walls at a depth \(D\) below the surface of the water. The horizontal distance \({x}\) in terms of \(H\) and \({D}\) is:
    
1. \(x = \sqrt{D\left(H-D\right)}\)
2. \(x = \sqrt{\frac{D \left(H - D \right)}{2}}\)
3. \(x = 2 \sqrt{D \left(H-D\right)}\)
4. \(x = 4 \sqrt{D \left(H-D\right)}\)

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 figure 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 \(2~\text{cm},1~\text{cm}\) and \(2~\text{cm}.\) It can be said that:

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 \(10 ^3~\text{kg/m}^3 \) and \(1 ~\text{atm pressure} = 10 ^5~\text{N/m}^ 2 . \) The speed of water coming out of the orifice is: 
1. \(10~\text{m/s}\)
2. \(20~\text{m/s}\)
3. \(10\sqrt{6}~\text{m/s}\)
4. \(10\sqrt{2}~\text{m/s}\)

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

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 airplane is \(50~\text{m/s}.\) What speed of flow over the upper surface will give a dynamic lift of \(1000~\text{Pa}?\) 
(density of air \(1.3~\text{kg/m}^3\) )
                 
1. \(25.55~\text{m/s}\)
2. \(63.55~\text{m/s}\)
3. \(13.25~\text{m/s}\)
4. \(6.35~\text{m/s}\)

The water flows through a frictionless tube with a varying cross-section as shown in the figure. The variation of pressure \(P\) at the 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. \(\dfrac{1}{2} m v^{3}\)                                   

2. \(m v^{3}\)

3. \(\dfrac{1}{2} m v^{2}\)                                   

4. \(\dfrac{1}{2} m^{2} v^{2}\)