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 $\frac{\mathrm{A}}{4}$, The pressure at P is 2.8 x 10${}^5$ Pa.)
      
1. 2.36 x 10${}^5$ Pa
2. 3.88 x 10${}^5$ Pa
3. 2.08 x 10${}^5$ Pa
4. 1.72 x 10${}^5$ 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. $2\times {10}^{-3}$ $\mathrm{J}/\mathrm{kg}$

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

A tank is filled with water up to a height h and the pressure at the bottom of the tank is 3P where P is the atmospheric pressure. The height of a point from the bottom of the tank where pressure is $\frac{11\mathrm{P}}{5}$ is:

1. $\frac{2\mathrm{h}}{5}$

2. $\frac{3\mathrm{h}}{5}$

3. $\frac{4\mathrm{h}}{5}$

4. None of these

A body of density 0.7 gm/${\mathrm{cm}}^3$ floats on a lake of water. The fraction of the body which is outside water is-

1. 30%

2. 70%

3. 25%

4. 50%

A small spherical solid ball is dropped in a viscous liquid. Its journey in the liquid is best described in the figure by:
                        

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.

Equation of continuity is based on:

An inverted bell lying at the bottom of a lake 47.6 m deep has 50 cm³ of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be: (atmospheric pressure = 70 cm of Hg and density of Hg = 13.6 g/cm³) 

1. 350 cm³                               

2. 300 cm³

3. 250 cm³                               

4. 22 cm³

A siphon in use is demonstrated in the following figure. The density of the liquid flowing in the siphon is 1.5 gm/cc. The pressure difference between the point P and S will be: