Mechanical Properties of Fluids Chapter-Wise Test 11

Correct answer Carries: 4.

Wrong Answer Carries: -1.

Why is the pressure of the atmosphere measured as the weight of a column of air?

Atmospheric pressure is the weight of the air column per unit area above a point, extending to the top of the atmosphere, as it results from the gravitational force acting on the air mass, as described in the chapter.

Due to air viscosity
Because of surface tension
It’s the weight of air per unit area
Due to streamline flow
3

What assumption does Bernoulli’s principle make about fluid flow that limits its application to real fluids?

Bernoulli’s principle assumes zero viscosity (non-viscous flow), ignoring frictional losses that occur in real fluids, where viscosity converts kinetic energy into heat, reducing its applicability.

Fluid is compressible
Zero viscosity
Turbulent flow
Constant density
2

A hydraulic system has a small piston (\( 0.005 \, \text{m}^2 \)) and a large piston (\( 0.025 \, \text{m}^2 \)). If \( 80 \, \text{N} \) is applied on the small piston, what force does the large piston exert?

Pascal’s law: \( P = \frac{F_1}{A_1} = \frac{F_2}{A_2} \).

\( F_2 = F_1 \times \frac{A_2}{A_1} \).

\( F_1 = 80 \, \text{N} \), \( A_1 = 0.005 \, \text{m}^2 \), \( A_2 = 0.025 \, \text{m}^2 \).

\( F_2 = 80 \times \frac{0.025}{0.005} = 80 \times 5 = 400 \, \text{N} \).

300 N
350 N
400 N
450 N
3

A \( 75 \, \text{kg} \) person stands on two bones, each with area \( 24 \, \text{cm}^2 \). What is the average pressure on the bones? (Take \( g = 9.8 \, \text{m/s}^2 \))

\( P_{av} = \frac{F}{A} \), \( F = mg = 75 \times 9.8 = 735 \, \text{N} \).

Total area \( A = 2 \times 24 \times 10^{-4} = 4.8 \times 10^{-3} \, \text{m}^2 \).

\( P_{av} = \frac{735}{4.8 \times 10^{-3}} = 1.53125 \times 10^5 \, \text{Pa} \).

1.4 × 10⁵ Pa
1.5 × 10⁵ Pa
1.53 × 10⁵ Pa
1.6 × 10⁵ Pa
3

A pipe has a cross-sectional area of \( 0.02 \, \text{m}^2 \) at one end and \( 0.01 \, \text{m}^2 \) at the other. If water flows at \( 2 \, \text{m/s} \) through the wider end, what is the speed at the narrower end?

Using the equation of continuity: \( A_1 v_1 = A_2 v_2 \).

\( A_1 = 0.02 \, \text{m}^2 \), \( v_1 = 2 \, \text{m/s} \), \( A_2 = 0.01 \, \text{m}^2 \).

\( v_2 = \frac{A_1 v_1}{A_2} = \frac{0.02 \times 2}{0.01} = 4 \, \text{m/s} \).

1 m/s
2 m/s
4 m/s
8 m/s
3

What ensures that the braking effort is equal on all wheels in a hydraulic brake system?

Pascal’s law ensures that pressure applied to the brake fluid is transmitted undiminished to all brake cylinders, providing equal force to each wheel, as the system relies on uniform pressure distribution.

Viscosity of the fluid
Surface tension
Equal pressure transmission
Streamline flow
3

A spray tube (\( 4 \, \text{cm}^2 \)) has 20 holes of diameter \( 1.4 \, \text{mm} \). If the flow speed is \( 1.8 \, \text{m/min} \), what is the ejection speed?

\( A_1 v_1 = A_2 v_2 \), \( v_1 = 1.8 \, \text{m/min} = 0.03 \, \text{m/s} \), \( A_1 = 4 \times 10^{-4} \, \text{m}^2 \).

Hole area: \( A_h = \pi (0.7 \times 10^{-3})^2 \), total \( A_2 = 20 \times \pi \times 4.9 \times 10^{-7} \approx 3.079 \times 10^{-5} \, \text{m}^2 \).

\( v_2 = \frac{4 \times 10^{-4} \times 0.03}{3.079 \times 10^{-5}} \approx 0.39 \, \text{m/s} \).

0.3 m/s
0.39 m/s
0.45 m/s
0.5 m/s
2

Which statement is incorrect about the Magnus effect?

The Magnus effect causes a spinning object to deviate due to a pressure difference from varying air speeds (Bernoulli’s principle), not viscosity or gravity alone. The incorrect statement is that it’s due to gravitational force.

It involves pressure differences
It applies to spinning objects
It is due to gravitational force
It relates to Bernoulli’s principle
3

A \( 55 \, \text{kg} \) person stands on two bones, each with area \( 14 \, \text{cm}^2 \). What is the average pressure on the bones? (Take \( g = 10 \, \text{m/s}^2 \))

\( P_{av} = \frac{F}{A} \), \( F = mg = 55 \times 10 = 550 \, \text{N} \).

Total area \( A = 2 \times 14 \times 10^{-4} = 2.8 \times 10^{-3} \, \text{m}^2 \).

\( P_{av} = \frac{550}{2.8 \times 10^{-3}} = 1.964 \times 10^5 \, \text{Pa} \).

1.8 × 10⁵ Pa
1.96 × 10⁵ Pa
2.0 × 10⁵ Pa
2.2 × 10⁵ Pa
2

Which of the following statements is correct about a barometer?

A barometer measures atmospheric pressure by balancing it with the weight of a liquid column (\( P_a = \rho g h \)), typically mercury due to its high density, which shortens the column height.

It measures fluid viscosity
It uses water for accuracy
It measures atmospheric pressure
It depends on surface tension
3

Why do liquid drops tend to be spherical in the absence of external forces?

Surface tension minimizes surface energy by reducing surface area. For a given volume, a sphere has the smallest surface area, making it the preferred shape for liquid drops when gravity or other forces are negligible.

Due to viscosity
Because of pressure inside
Surface tension minimizes surface area
Due to buoyancy
3

A capillary tube of radius \( 0.25 \, \text{mm} \) is dipped in ethanol (\( S = 0.0227 \, \text{N/m} \), \( \rho = 806 \, \text{kg/m}^3 \), \( \cos \theta = 1 \)). What is the capillary rise? (Take \( g = 9.8 \, \text{m/s}^2 \))

\( h = \frac{2 S \cos \theta}{\rho g a} \).

\( S = 0.0227 \, \text{N/m} \), \( \rho = 806 \, \text{kg/m}^3 \), \( g = 9.8 \, \text{m/s}^2 \), \( a = 0.25 \times 10^{-3} \, \text{m} \).

\( h = \frac{2 \times 0.0227 \times 1}{806 \times 9.8 \times 0.25 \times 10^{-3}} = 0.02298 \, \text{m} = 2.3 \, \text{cm} \).

1.5 cm
2.3 cm
3.0 cm
4.0 cm
2

A tank has a hole \( 1.7 \, \text{m} \) below the water surface, open to the atmosphere. What is the efflux speed? (Take \( g = 9.8 \, \text{m/s}^2 \))

Torricelli’s law: \( v = \sqrt{2 g h} \).

\( g = 9.8 \, \text{m/s}^2 \), \( h = 1.7 \, \text{m} \).

\( v = \sqrt{2 \times 9.8 \times 1.7} = \sqrt{33.32} \approx 5.77 \, \text{m/s} \).

5.2 m/s
5.5 m/s
5.8 m/s
6.0 m/s
3

A bubble of radius \( 4.5 \, \text{mm} \) is blown at \( 35 \, \text{cm} \) depth in a soap solution (\( \rho = 1.2 \times 10^3 \, \text{kg/m}^3 \), \( S = 0.025 \, \text{N/m} \)). What is the total pressure inside? (Take \( P_a = 1.01 \times 10^5 \, \text{Pa} \), \( g = 9.8 \, \text{m/s}^2 \))

\( P_i = P_a + \rho g h + \frac{2 S}{r} \).

\( P_a = 1.01 \times 10^5 \, \text{Pa} \), \( \rho g h = 1.2 \times 10^3 \times 9.8 \times 0.35 = 4116 \, \text{Pa} \).

\( \frac{2 S}{r} = \frac{2 \times 0.025}{4.5 \times 10^{-3}} = 11.11 \, \text{Pa} \).

\( P_i = 1.01 \times 10^5 + 4116 + 11.11 = 1.05127 \times 10^5 \, \text{Pa} \).

1.04 × 10⁵ Pa
1.05 × 10⁵ Pa
1.06 × 10⁵ Pa
1.07 × 10⁵ Pa
2

Why is pressure considered a scalar quantity despite being defined as force per unit area?

Pressure is a scalar because it acts equally in all directions in a fluid at rest and lacks directional properties, even though force (a vector) is involved. Only the normal component of force is considered in its definition (\( P = F/A \)).

It depends on direction
Force is a scalar
It acts equally in all directions
Area is a vector
3

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