In which one of the following cases will the liquid flow in a pipe be most streamlined  ?

1. Liquid of high viscosity and high density flowing through a pipe of small radius

2. Liquid of high viscosity and low density flowing through a pipe of small radius

3. Liquid of low viscosity and low density flowing through a pipe of large radius

4. Liquid of low viscosity and high density flowing through a pipe of large radius

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

The following figure shows the flow of liquid through a horizontal pipe. Three tubes \(A,\) \(B\) and \(C\) are connected to the pipe. The radii of the tubes  \(A,\) \(B\) and \(C\) at the junction are respectively \(2\) cm, \(1\) cm and \(2\) cm. It can be said that:

A manometer connected to a closed tap reads $3.5\times {10}^5 \mathrm{N}/{\mathrm{m}}^2$. When the valve is opened, the reading of manometer falls to $3.0\times {10}^5 \mathrm{N}/{\mathrm{m}}^2$ , then velocity of flow of water is

1. 100 m/s                                       

2. 10 m/s

3. 1 m/s                                           

4. $10\sqrt{10}$ m/s

A large tank filled with water to a height ‘h’ is to be emptied through a small hole at the bottom. The ratio of time taken for the level of water to fall from h to $\frac{\mathrm{h}}{2}$ and from $\frac{\mathrm{h}}{2}$ to zero is

1. $\sqrt{2}$                                               

2. $\frac{1}{\sqrt{2}}$

3. $\sqrt{2}-1$                                         

4. $\frac{1}{\sqrt{2}-1}$

A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in m/s) through a small hole on the side wall of the cylinder near its bottom is

1. 10                                       

2. 20

3. 25.5                                     

4. 5

There is a hole in the bottom of a tank having water. If the total pressure at the bottom is \(3\) atm \((1~\text{atm}=10^5~\text{N}/\text{m}^2),\) then the velocity of water flowing from the hole is:
1. \(\sqrt{400}~~\text{m/s}\)
2. \(\sqrt{600}~~\text{m/s}\)
3. \(\sqrt{60}~~\text{m/s}\)
4. none of these

A square plate of 0.1 m side moves parallel to a second plate with a velocity of 0.1 m/s, both plates being immersed in water. If the viscous force is 0.002 N and the coefficient of viscosity is 0.01 poise, then the distance between the plates in m is:

A spherical ball of radius \(r\) is falling in a viscous fluid of viscosity \(\eta\) with a velocity \(v.\) The retarding viscous force acting on the spherical ball is:

A ball of radius r and density $\mathrm{\rho }$ falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is $\mathrm{\eta }$, the value of h( in CGS units) is given by-

1. $\frac{2}{9}{\mathrm{r}}^2\left(\frac{1-\mathrm{\rho }}{\mathrm{\eta }}\right)\mathrm{g}$

2. $\frac{2}{81}{\mathrm{r}}^2\left(\frac{\mathrm{\rho }-1}{\mathrm{\eta }}\right)\mathrm{g}$

3. $\frac{2}{81}{\mathrm{r}}^4{\left(\frac{\mathrm{\rho }-1}{\mathrm{\eta }}\right)}^2\mathrm{g}$

4. $\frac{2}{9}{\mathrm{r}}^4{\left(\frac{\mathrm{\rho }-1}{\mathrm{\eta }}\right)}^2\mathrm{g}$