Water flows through a frictionless duct with a cross-section varying as shown in the figure. Pressure \(P\) at points along the axis is represented by:

     

1.		2.
3.		4.

Three liquids of densities \(d,\) \(2d\) and \(3d\) are mixed in equal proportions of weights. The relative density of the mixture is: 

Find the rate of flow of glycerin of density 1.25 × 10³ kg/m³ through the conical section of a pipe, if the radii of its ends are 0.1 m and 0.04 m and the pressure drop across its length is 10 N/m².
1. 3.14 × 10^–4 m³/s 
2. 6.28 × 10^–4 m³/s
3. 12.56 × 10^–4 m³/s 
4. 1.57 × 10^–4 m³/s

A liquid drop at temperature T, isolated from its surroundings, breaks into a number of droplets. The temperature of the droplets will be–

Fluid flows through a pipe in a horizontal plane. The fluid has a relative density of \(0.9\) and its velocity at \(P\) (where cross-section area is \(A\)) is \(4\) m/s. What is its pressure at \(Q\)? (where cross-section area is \(\frac{A}{4},\) The pressure at \(P\) is \(2.8\times 10^{5}~\text{Pa})\)
      
1. \(2.36\times 10^{5}~\text{Pa}\)
2. \(3.88\times 10^{5}~\text{Pa}\)
3. \(2.08\times 10^{5}~\text{Pa}\)
4. \(1.72\times 10^{5}~\text{Pa}\)

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 diver is \(10\) m below the surface of the water. The approximate pressure experienced by the diver is:
1. \(10^5\) Pa                   
2. \(2\times10^5\) Pa
3. \(3\times10^5\) Pa       
4. \(4\times 10^5\) Pa

A mercury-filled U–tube arrangement is connected to a bulb containing a gas. Atmospheric pressure is \(1.012 \times 10^5\) Pa and \(\mathrm{H}=0.05\) m.
    
Then:

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

When two drops of water coalesce:

Which of the following is correct?