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. \(2~\text{m/s}\) 

If an incompressible liquid is flowing through a horizontal pipe having branches of area \({A},\) \(0.4{A},\) and \(0.5{A}\) as shown in the figure, then the value of \({v}\) is:
                                  
1. \(3.2~\text{m/s}\)
2. \(6.4~\text{m/s}\)
3. \(1.6~\text{m/s}\)
4. \(0.8~\text{m/s}\)

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. \(32\)

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:

The diameter of a syringe is \(4~\text{mm}\) and the diameter of its nozzle (opening) is \(1~\text{mm}\). The syringe is placed on the table horizontally at a height of \(1.25~\text{m}\). If the piston is moved at a speed of \(0.5~\text{m/s}\), then considering the liquid in the syringe to be ideal, the horizontal range of liquid is: \(\left(g = 10~\text{m/s}^2 \right)\)
1. \(4~\text{m}\)
2. \(8~\text{m}\)
3. \(0.4~\text{m}\)
4. \(0.2~\text{m}\)

Equation of continuity is based on:

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.