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 based on :

1.  Conservation of mass

2.  Conservation of energy

3.  Conservation of angular momentum

4.  None of these

The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is v, the speed of the ejection of the liquid through the holes is

1. $\frac{{\mathrm{vR}}^2}{{\mathrm{n}}^2{\mathrm{r}}^2}$

2. $\frac{{\mathrm{vR}}^2}{{\mathrm{nr}}^2}$

3. $\frac{{\mathrm{vr}}^2}{{\mathrm{n}}^2{\mathrm{R}}^2}$

4. $\frac{{\mathrm{v}}^2\mathrm{R}}{\mathrm{nr}}$

The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is v, then the speed of ejection of the liquid through the holes will be:
1. vR²/n²r²

2. vR²/nr²

3. vR²/n³r²

4. v²R/nr

Two water pipes of diameters 2 cm and 4 cm are connected with the main supply line. The velocity of flow of water in the pipe of 2 cm diameter is -

(1) 4 times that in the other pipe

(2) 3 times that in the other pipe

(3) 2 times that in the other pipe

(4) 6 times that in the other pipe

An incompressible liquid flows through a horizontal tube as shown in the following fig. Then the velocity v of the fluid is

(1)    3.0 m/s                          

(2) 1.5 m/s                     

(3) 1.0 m/s                             

(4) 2.25 m/s

Water is flowing through a tube of the non-uniform cross-section. The ratio of the radius at the entry and exit end of the pipe is \(3:2\). Then the ratio of velocities at entry and exit of liquid is:
1. \(4:9\)                         
2. \(9:4\) 
3. \(8:27\)                         
4. \(1:1\)

A liquid flows in a tube from left to right as shown in figure. ${\mathrm{A}}_1$ and ${\mathrm{A}}_2$ are the cross-sections of the portions of the tube as shown. Then the ratio of speeds ${\mathrm{v}}_1/{\mathrm{v}}_2$ will be

(1) ${\mathrm{A}}_1/{\mathrm{A}}_2$

(2) ${\mathrm{A}}_2/{\mathrm{A}}_1$

(3) $\sqrt{{\mathrm{A}}_2}/\sqrt{{\mathrm{A}}_1}$

(4) $\sqrt{{\mathrm{A}}_1}/\sqrt{{\mathrm{A}}_2}$

Water is flowing in a pipe of diameter 4 cm with a velocity 3 m/s. The water then enters into a tube of diameter 2 cm. The velocity of water in the other pipe is
(1) 3 m/s                                       

(2) 6 m/s

(3) 12 m/s                                       

(4) 8 m/s

An incompressible fluid flows steadily through a cylindrical pipe which has a radius 2r at point A and a radius r at B further along the flow direction. If the velocity at point A is v, its velocity at point B is:
1. 2v                               
2. v
3. v/2                               
4. 4v