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:

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 the point \(A\) and a radius \(r\) at the point \(B\) further along the flow direction. If the velocity at the point \(A\) is \(v,\) its velocity at the point \(B\) is:
1. \(2v\)                               
2. \(v\)
3. \(v/2\)                            
4. \(4v\)