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

A liquid is flowing in a horizontal uniform capillary tube under a constant pressure difference P. The value of pressure for which the rate of flow of the liquid is doubled when the radius and length both are doubled is

1. P                             

2. $\frac{3\mathrm{P}}{4}$

3. $\frac{\mathrm{P}}{2}$                           

4. $\frac{\mathrm{P}}{4}$

We have two (narrow) capillary tubes T₁ and T₂. Their lengths are l₁ and l₂ and radii of cross-section are r₁ and r₂ respectively. The rate of flow of water under a pressure difference P through tube T₁ is 8cm³/sec. If l₁ = 2l₂ and r₁ =r₂, what will be the rate of flow when the two tubes are connected in series and pressure difference across the combination is same as before (= P)

1. 4 cm³/sec                           

2. (16/3) cm³/sec

3. (8/17) cm³/sec                   

4. None of these

The Reynolds number of a flow is the ratio of

1. Gravity to viscous force

2. Gravity force to pressure force

3. Inertia forces to viscous force

4. Viscous forces to pressure forces