Fluid Mechanics

Q. The velocity profile in fully developed laminar flow in a pipe of diameter D is given by $u=u_0(1-4r^2/D^2)$, where r is the radial distance from the center. If the viscosity of the fluid is $\mu$, the pressure drop across a length L of the pipe is

1. $\frac{\mu u_{0}L}{D^2}$
2. $\frac{4\mu u_{0}L}{D^2}$
3. $\frac{8\mu u_{0}L}{D^2}$
4. $\frac{16\mu u_{0}L}{D^2}$

Q. An inverted U-tube manometer is used to measure the pressure difference between two pipes A and B, as shown in the figure. Pipe A is carrying oil(specific gravity=0.8) and pipe B is carrying water. The densities of air and water are 1.16 kg/$m^3$ and 1000 kg/$m^3$, respectively. The pressure difference between pipes A and B is _____kPa.
Acceleration due to gravity:g = 10 m/$s^2$

1. -2.199

Q. $\text{The discharge over a}{90}^{\circ }\text{V-notch is given as}Q=1.37H^{\frac{5}{2}}{\text{, where Q is in m}}^3\text{/s and H in m, the}{C}_d\text{of the notch is}$

1. 0.611
2. 0.580
3. 0.464
4. 0.710

Q. The velocity distribution for flow between two fixed parallel plates

1. is constant over the cross-section
2. is zero at the plates and increases linearly to the mid-plane
3. varies parabolically across the section
4. is zero in middle and increases linearly towards the plates

Q. The discharge over a broad crested weir is maximum when the depth of flow is

1. $\frac{H}{3}$
2. $\frac{2H}{3}$
3. $\frac{H}{2}$
4. $\frac{2H}{5}$

Q.

The S.I unit of viscosity is _________.

Q. A horizontal venturimeter with inlet diameter of 30 cm and throat diameter of 15 cm is used to measure the flow of water. The reading on a differential manometer connected to the inlet and the throat is 20 cm of mercury. If $C_d=0.98$, the rate of flow is nearly

1. 12.5 l/s
2. 25 l/s
3. 125 l/s
4. 250 l/s

Q.

A streamlined body:

1. Increases friction

2. Reduces friction

3. Decreases weight

4. Increases weight

Q. The difference in pressure head, measured by a mercury water differential manometer for a 20 cm difference of mercury head will be

1. 2.72 m
2. 2.52 m
3. 2.0 m
4. 0.2 m

Q. The Bernoulli's equation is applicable to:

1. Both steady and unsteady flows
2. Real fluids
3. All fluids and flow along a stream tube
4. Steady flow of ideal fluids along a stream tube

Q. The velocity distribution for turbulent flow through circular pipe is

1. Uniform
2. Linear
3. Parabolic
4. Logarithmic

Q.

Are vapour pressure and saturation pressure are the same?

Q. The stream function in a two dimensional flow field is given by $\psi =x^2-y^2$ . The magnitude of the velocity at point (1, 1) is

1. 2
2. 2$\sqrt{2}$
3. 4
4. 8

Q. A mercury manometer is used to measure the static pressure at a point in a water pipe as shown in figure. The level difference of mercury in the two limbs is 10 mm. The gauge pressure at that point is

1. 1236 Pa
2. 1333 Pa
3. Zero
4. 98 Pa

Q. A vertical triangular plane area, submerged in water, with one side in the free surface, vertex downward and latitude 'h' has the pressure centre below the free surface by

1. h/4
2. h/3
3. 2h/3
4. h/2

Q. As depth of immersion of a vertical plane surface increases, the location of centre of pressure

1. comes closer to the centre of gravity of the area
2. moves apart from the centre of gravity of the area
3. ultimately coincides with the centre of gravity of the area
4. remains unaffected

Q. An isosceles triangular plate of base 3 m and altitude 3 m is immersed vertically in an oil of specific gravity 0.8. The base of the plate coincides with the free surface of oil. The centre of pressure will lie at a distance of (from free surface)

1. 2.5 m
2. 2 m
3. 1.5 m
4. 1 m

Q. If a water tank, partially filled with water is being carried on a truck, moving with a constant horizontal acceleration, the level of liquid will

1. Rise and fall alternately on the front side of the tank
2. Fall on the rear side of the tank
3. Remain the same on both sides of the tank
4. Rise on the rear side and fall on the front side of the tank

Q. A horizontal water jet with a velocity of 10 m/s and cross-sectional area of 10 mm${}^2$ strikes a flat plate held normal to the flow direction. The density of water is 1000kg/$m^3$. The total force on the plate due to the jet is

1. 100N
2. 10 N
3. 1 N
4. 0.1 N

Q.

Water flows into a large tank with a flat bottom at the rate of ${10}^{-4}{m}^3{s}^{-1}$. Water is also leaking out of a hole of area $1c{m}^2$ at its bottom. If the height of the water in the tank remains steady, then this height is

1. $5.1cm$

2. $4cm$

3. $2.9cm$

4. $1.7cm$

Q. A solid cylinder of length L, diameter D and specific gravity 0.6 floats in neutral equilibrium in water with its axis vertical. What is the ratio of L to D?

1. $\frac{\sqrt{3}}{2}$
2. $\frac{2\sqrt{3}}{5}$
3. $\frac{4}{5\sqrt{3}}$
4. $\frac{5}{4\sqrt{3}}$

Q. Calculate the kinematic viscosity (stokes) of the fluid if the dynamic viscosity of fluid is 0.5 poise and specific gravity is 0.4?

1. $0.95$
2. $1$
3. $1.25$
4. $1.5$

Q. A venturimeter, having a diameter of 7.5 cm at the throat and 15 cm at the enlarged end, is installed in a horizontal pipeline of 15 cm diameter. The pipe carries an incompressible fluid at a steady rate of 30 litres per second. The difference of pressure head measured in terms of the moving fluid in between the enlarged and the throat of the venturimeter is observed to be 2.45 m. Taking the acceleration due to gravity as 9.81 m/s${}^2$, the coefficient of discharge of the venturimeter (correct up to two places of decimal) is

1. 0.95

Q. The Chezy's coefficient C is related to Darcy-Weisbach friction factor 'f' as

1. $C=\sqrt{\left(\frac{g}{8f}\right)}$
2. $C=\sqrt{\left(\frac{8g}{f^{\frac{1}{4}}}\right)}$
3. $C=\sqrt{\left(\frac{8g}{f}\right)}$
4. $C=\sqrt{\left(\frac{f}{8g}\right)}$

Q. Poise has the unit of

1. Dyne-cm/$s^2$
2. Dyne-cm/s
3. Dyne-s/cm
4. Dyne-s/c$m^2$

Q. For a two-dimensional irrotational flow, the velocity potential is defined as $\varphi =lo{g}_e(x^2+y^2)$. Which of the following is a possible stream function, $\psi$, for this flow?

1. $\frac{1}{2}ta{n}^{-1}\left(y/x\right)$
2. $ta{n}^{-1}\left(y/x\right)$
3. $2ta{n}^{-1}\left(y/x\right)$
4. $2ta{n}^{-1}\left(x/y\right)$

Q. A pitot-static tube, with a coefficient of 0.98 is used to measure the velocity of water in a pipe. The stagnation pressure recorded is 3m and the static pressure is 0.5 m. What is the velocity of flow?

1. 7.2 m/s
2. 6.8 m/s
3. 5.9 m/s
4. 5.2 m/s

Q. The stable equilibrium is achieved in the floating body when ?

1. Center of gravity is below the center of buoyancy.
2. Metacenter is above the center of gravity.
3. Metacenter is below the center of gravity.
4. Metacentric height is zero.

Q. For air flow over a flat plate, velocity (U) and boundary layer thickness ($\delta$) can be expressed respectively, as

$\frac{u}{u_{\infty }}=\frac{3}{2}\frac{y}{\delta }-\frac{1}{2}{\left(\frac{y}{\delta }\right)}^3;$ $\delta =\frac{4.64x}{\sqrt{R{e}_x}}$

If the free stream velocity is 2 m/s and air has kinematic viscosity of 1.5$\times {10}^{-5}{m}^2/s$ and density of 1.23 kg/$m^3$, the wall shear stress at x = 1 m, is

1. $2.36\times {10}^{2}N/m^2$
2. $43.6\times {10}^{-3}N/m^2$
3. $4.36\times {10}^{-3}N/m^2$
4. $2.18\times {10}^{-3}N/m^2$

Q. The thickness of the laminar boundary layer over a flat plate at two different sections P and Q are 0.8 cm and 2.4 cm respectively. If the section Q is 3.6 m downstream of P, the distance of section P from the leading edge of the plate is

1. 0.32 m
2. 0.22 m
3. 0.40 m
4. 0.53 m