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

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

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

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. \(\dfrac{vR^2}{n^2r^2}\)

2. \(\dfrac{vR^2}{nr^2}\)

3. \(\dfrac{vR^2}{n^3r^2}\)

4. \(\dfrac{v^2R}{nr}\)

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.

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. \(0.2~\text{m}\)