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. \(4v\)

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:

In a horizontal pipe of a non-uniform cross-section, water flows with a velocity of \(1~\text{ms}^{-1}\)${\mathrm{}}^{}$ at a point where the diameter of the pipe is \(20 ~\text{cm}.\) The velocity of water \((\text{ms}^{-1})\) at a point where the diameter of the pipe is \(5~\text{cm}\) is:
1. \(8\)
2. \(16\)
3. \(24\)
4. \(32\)

From the given diagram, what is the velocity \(v_3?\)
               
1. \(4~\text{m/s}\)
2. \(3~\text{m/s}\)
3. \(1~\text{m/s}\)
4. \(2~\text{m/s}\) 

The fluid is in streamlined flow through a horizontal pipe with a variable cross-sectional area. Which of the following statements is correct?

The cylindrical tube of a spray pump has a cross-section of \(8.0\) cm² one end of which has \(40\) fine holes each of diameter \(1.0\) mm. If the liquid flow inside the tube is \(1.5\) m-min^–1,  the speed of ejection of the liquid through the holes is:
1. \(0.64\) ms^-1
2. \(0.74\) ms^-1
3. \(0.54\) ms^-1
4. \(0.84\) ms^-1

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. \(1:1\)