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

The continuity equation for fluid flow is based on the principle of the

(1) Conservation of mass

(2) Conservation of energy

(3) Conservation of momentum

(4) Conservation of angular momentum

Blood flows in an artery of radius R in a Laminar manner under pressure p with a flow rate Q. If the radius gets halved and the pressure quadruples, the new rate of flow will be

1.  4Q

2.  $\frac{\mathrm{Q}}{4}$

3.  Q

4.  $\frac{Q}{8}$

A sphere of mass M and radius R is falling in a viscous liquid. The terminal velocity attained by the sphere will be proportional to:

(1) ${\mathrm{R}}^2$

(2) R

(3) $\frac{1}{\mathrm{R}}$

(4) $\frac{1}{{\mathrm{R}}^2}$

Two water droplets merge with each other to form a larger droplet isothermally. In this process

(1) Energy is absorbed

(2) Energy is liberated

(3) Energy is neither liberated nor absorbed

(4) Some mass is converted into energy

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 value of Reynold's number for which the flow of water through a pipe becomes turbulent is:

(1) 500

(2) 900

(3) 750

(4) 3000

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

A lead sphere of mass \(m\) falls in a viscous liquid with terminal velocity \(v\). Another lead sphere of mass \(M\) falls through the liquid with terminal velocity \(4v\). The ratio \(\frac{M}{m}\) is:
1. \(2\)
2. \(4\)
3. \(8\)
4. \(16\)

In the given figure, the velocity ${\mathrm{v}}_3$ of inc fluid flowing through the tube will be

(1) 3 m/s

(2) 4,5 m/s

(3) 3.5 m/s

(4) 5 m/s