Mechanical Properties of Fluids Chapter-Wise Test 3

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A soap bubble of radius \( 7 \, \text{mm} \) has an excess pressure of \( 20 \, \text{Pa} \) inside. What is its surface tension?

Excess pressure in a bubble: \( \Delta P = \frac{4 S}{r} \).

\( \Delta P = 20 \, \text{Pa} \), \( r = 7 \times 10^{-3} \, \text{m} \).

\( S = \frac{\Delta P \cdot r}{4} = \frac{20 \times 7 \times 10^{-3}}{4} = 0.035 \, \text{N/m} \).

0.030 N/m
0.032 N/m
0.034 N/m
0.035 N/m
4

A soap bubble of radius \( 8 \, \text{mm} \) has a surface tension of \( 0.026 \, \text{N/m} \). What is the excess pressure inside?

Excess pressure in a bubble: \( \Delta P = \frac{4 S}{r} \).

\( S = 0.026 \, \text{N/m} \), \( r = 8 \times 10^{-3} \, \text{m} \).

\( \Delta P = \frac{4 \times 0.026}{8 \times 10^{-3}} = 13 \, \text{Pa} \).

10 Pa
12 Pa
13 Pa
15 Pa
3

A capillary tube of radius \( 0.45 \, \text{mm} \) is dipped in water (\( S = 0.0727 \, \text{N/m} \), \( \rho = 1000 \, \text{kg/m}^3 \), \( \cos \theta = 1 \)). What is the capillary rise? (Take \( g = 9.8 \, \text{m/s}^2 \))

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

\( S = 0.0727 \, \text{N/m} \), \( \rho = 1000 \, \text{kg/m}^3 \), \( g = 9.8 \, \text{m/s}^2 \), \( a = 0.45 \times 10^{-3} \, \text{m} \).

\( h = \frac{2 \times 0.0727 \times 1}{1000 \times 9.8 \times 0.45 \times 10^{-3}} = 0.03298 \, \text{m} = 3.3 \, \text{cm} \).

3.0 cm
3.3 cm
3.6 cm
3.9 cm
2

A bubble of radius \( 4.0 \, \text{mm} \) is blown at \( 60 \, \text{cm} \) 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 \( P_a = 1.01 \times 10^5 \, \text{Pa} \), \( g = 10 \, \text{m/s}^2 \))

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

\( P_a = 1.01 \times 10^5 \, \text{Pa} \), \( \rho g h = 1.2 \times 10^3 \times 10 \times 0.6 = 7200 \, \text{Pa} \).

\( \frac{2 S}{r} = \frac{2 \times 0.025}{4.0 \times 10^{-3}} = 12.5 \, \text{Pa} \).

\( P_i = 1.01 \times 10^5 + 7200 + 12.5 = 1.082125 \times 10^5 \, \text{Pa} \).

1.07 × 10⁵ Pa
1.08 × 10⁵ Pa
1.09 × 10⁵ Pa
1.10 × 10⁵ Pa
2

A capillary tube of radius \( 0.35 \, \text{mm} \) 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 \( g = 10 \, \text{m/s}^2 \))

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

\( S = 0.0227 \, \text{N/m} \), \( \rho = 806 \, \text{kg/m}^3 \), \( g = 10 \, \text{m/s}^2 \), \( a = 0.35 \times 10^{-3} \, \text{m} \).

\( h = \frac{2 \times 0.0227 \times 1}{806 \times 10 \times 0.35 \times 10^{-3}} = 0.0161 \, \text{m} = 1.61 \, \text{cm} \).

1.2 cm
1.6 cm
2.0 cm
2.4 cm
2

A \( 60 \, \text{kg} \) person stands on two cylindrical bones, each of cross-sectional area \( 15 \, \text{cm}^2 \). What is the average pressure on the bones? (Take \( g = 10 \, \text{m/s}^2 \))

\( P_{av} = \frac{F}{A} \), \( F = mg = 60 \times 10 = 600 \, \text{N} \).

Total area \( A = 2 \times 15 \times 10^{-4} = 3 \times 10^{-3} \, \text{m}^2 \).

\( P_{av} = \frac{600}{3 \times 10^{-3}} = 2 \times 10^5 \, \text{Pa} \).

1 × 10⁵ Pa
2 × 10⁵ Pa
3 × 10⁵ Pa
4 × 10⁵ Pa
2

Water (\( \rho = 1000 \, \text{kg/m}^3 \)) flows horizontally at \( 3.8 \, \text{m/s} \) with pressure \( 1.8 \times 10^5 \, \text{Pa} \). If the speed increases to \( 6.2 \, \text{m/s} \), what is the new pressure?

Bernoulli’s equation: \( P_1 + \frac{1}{2} \rho v_1^2 = P_2 + \frac{1}{2} \rho v_2^2 \).

\( P_1 = 1.8 \times 10^5 \, \text{Pa} \), \( v_1 = 3.8 \, \text{m/s} \), \( v_2 = 6.2 \, \text{m/s} \), \( \rho = 1000 \, \text{kg/m}^3 \).

\( P_2 = 1.8 \times 10^5 + \frac{1}{2} \times 1000 (14.44 - 38.44) = 1.8 \times 10^5 - 12000 = 1.68 \times 10^5 \, \text{Pa} \).

1.65 × 10⁵ Pa
1.68 × 10⁵ Pa
1.70 × 10⁵ Pa
1.75 × 10⁵ Pa
2

Which of the following statements is correct regarding Pascal’s law?

Pascal’s law states that pressure applied to an enclosed fluid is transmitted undiminished to all parts, making it the basis for hydraulic systems, not dependent on fluid velocity or viscosity.

It applies only to moving fluids
Pressure is transmitted undiminished
It depends on fluid viscosity
It varies with container shape
2

A hydraulic lift raises a \( 1400 \, \text{kg} \) load using a small piston of radius \( 2.5 \, \text{cm} \) and a large piston of radius \( 10 \, \text{cm} \). What force is applied on the small piston? (Take \( g = 9.8 \, \text{m/s}^2 \))

\( F_1 = \frac{A_1}{A_2} F_2 \), \( F_2 = 1400 \times 9.8 = 13720 \, \text{N} \).

\( A_1 = \pi (0.025)^2 \), \( A_2 = \pi (0.1)^2 \), \( \frac{A_1}{A_2} = \frac{0.000625}{0.01} = \frac{1}{16} \).

\( F_1 = \frac{13720}{16} = 857.5 \, \text{N} \approx 858 \, \text{N} \).

700 N
858 N
900 N
1000 N
2

What is the gauge pressure at a depth of \( 0.9 \, \text{m} \) in whole blood (\( \rho = 1.06 \times 10^3 \, \text{kg/m}^3 \))? (Take \( g = 10 \, \text{m/s}^2 \))

Gauge pressure: \( P_g = \rho g h \).

\( \rho = 1.06 \times 10^3 \, \text{kg/m}^3 \), \( g = 10 \, \text{m/s}^2 \), \( h = 0.9 \, \text{m} \).

\( P_g = 1.06 \times 10^3 \times 10 \times 0.9 = 9540 \, \text{Pa} \).

8500 Pa
9540 Pa
10000 Pa
11000 Pa
2

What causes a liquid to form a concave meniscus in a glass tube?

A concave meniscus forms when adhesive forces between the liquid (e.g., water) and glass exceed cohesive forces within the liquid, pulling the edges upward and creating a curved surface.

High viscosity
Low density
Strong adhesive forces
Weak surface tension
3

A spray tube (\( 6 \, \text{cm}^2 \)) has 30 holes of diameter \( 1.1 \, \text{mm} \). If the flow speed is \( 3.6 \, \text{m/min} \), what is the ejection speed?

\( A_1 v_1 = A_2 v_2 \), \( v_1 = 3.6 \, \text{m/min} = 0.06 \, \text{m/s} \), \( A_1 = 6 \times 10^{-4} \, \text{m}^2 \).

Hole area: \( A_h = \pi (0.55 \times 10^{-3})^2 \), total \( A_2 = 30 \times \pi \times 3.025 \times 10^{-7} \approx 2.851 \times 10^{-5} \, \text{m}^2 \).

\( v_2 = \frac{6 \times 10^{-4} \times 0.06}{2.851 \times 10^{-5}} \approx 1.26 \, \text{m/s} \).

1.0 m/s
1.2 m/s
1.3 m/s
1.5 m/s
3

A capillary tube of radius \( 0.1 \, \text{mm} \) is dipped in water (\( S = 0.073 \, \text{N/m} \), \( \rho = 1000 \, \text{kg/m}^3 \)). What is the height of capillary rise? (Take \( g = 10 \, \text{m/s}^2 \), \( \cos \theta = 1 \))

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

\( S = 0.073 \, \text{N/m} \), \( \rho = 1000 \, \text{kg/m}^3 \), \( g = 10 \, \text{m/s}^2 \), \( a = 0.1 \times 10^{-3} \, \text{m} \), \( \cos \theta = 1 \).

\( h = \frac{2 \times 0.073}{1000 \times 10 \times 0.1 \times 10^{-3}} = 0.146 \, \text{m} = 14.6 \, \text{cm} \).

7.3 cm
14.6 cm
29.2 cm
58.4 cm
2

A hydraulic system applies \( 300 \, \text{N} \) on a small piston of area \( 0.015 \, \text{m}^2 \). What force is exerted by a large piston of area \( 0.045 \, \text{m}^2 \)?

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

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

\( F_1 = 300 \, \text{N} \), \( A_1 = 0.015 \, \text{m}^2 \), \( A_2 = 0.045 \, \text{m}^2 \).

\( F_2 = 300 \times \frac{0.045}{0.015} = 300 \times 3 = 900 \, \text{N} \).

800 N
850 N
900 N
950 N
3

A soap bubble of radius \( 10 \, \text{mm} \) has a surface tension of \( 0.025 \, \text{N/m} \). What is the excess pressure inside?

Excess pressure in a bubble: \( \Delta P = \frac{4 S}{r} \).

\( S = 0.025 \, \text{N/m} \), \( r = 10 \times 10^{-3} \, \text{m} \).

\( \Delta P = \frac{4 \times 0.025}{10 \times 10^{-3}} = 10 \, \text{Pa} \).

8 Pa
10 Pa
12 Pa
15 Pa
2

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