NEET Mechanical Properties of Fluids — Set 10

Question 1

A pipe’s cross-sectional area changes from $ 0.08 \, \text{m}^2 $ to $ 0.02 \, \text{m}^2 $. If the speed at the larger end is $ 1.2 \, \text{m/s} $, what is the speed at the smaller end?

Accepted Answer

Continuity equation: $ A_1 v_1 = A_2 v_2 $. $ A_1 = 0.08 \, \text{m}^2 $, $ v_1 = 1.2 \, \text{m/s} $, $ A_2 = 0.02 \, \text{m}^2 $. $ v_2 = \frac{A_1 v_1}{A_2} = \frac{0.08 \times 1.2}{0.02} = 4.8 \, \text{m/s} $.

Question 2

A manometer with ethyl alcohol ($ \rho = 806 \, \text{kg/m}^3 $) shows a height difference of $ 0.26 \, \text{m} $. What is the pressure difference? (Take $ g = 9.8 \, \text{m/s}^2 $)

Accepted Answer

$ \Delta P = \rho g h $. $ \rho = 806 \, \text{kg/m}^3 $, $ g = 9.8 \, \text{m/s}^2 $, $ h = 0.26 \, \text{m} $. $ \Delta P = 806 \times 9.8 \times 0.26 = 2055.08 \, \text{Pa} $.

Question 3

A capillary tube of radius $ 0.3 \, \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 = 10 \, \text{m/s}^2 $)

Accepted Answer

$ h = \frac{2 S \cos \theta}{\rho g a} $. $ S = 0.0727 \, \text{N/m} $, $ \rho = 1000 \, \text{kg/m}^3 $, $ g = 10 \, \text{m/s}^2 $, $ a = 0.3 \times 10^{-3} \, \text{m} $. $ h = \frac{2 \times 0.0727 \times 1}{1000 \times 10 \times 0.3 \times 10^{-3}} = 0.04847 \, \text{m} = 4.85 \, \text{cm} $.

NEET Physics: Mechanical Properties of Fluids — Practice Set 10

Q1. A pipe’s cross-sectional area changes from \( 0.08 \, \text{m}^2 \) to \( 0.02 \, \text{m}^2 \). If the speed at the larger end is \( 1.2 \, \text{m/s} \), what is the speed at the smaller end?

Q2. A manometer with ethyl alcohol (\( \rho = 806 \, \text{kg/m}^3 \)) shows a height difference of \( 0.26 \, \text{m} \). What is the pressure difference? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q3. A capillary tube of radius \( 0.3 \, \text{mm} \) 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 \( g = 10 \, \text{m/s}^2 \))

Q4. Water flows at \( 3.5 \, \text{m/s} \) at \( 4.5 \, \text{m} \) height with pressure \( 1.5 \times 10^5 \, \text{Pa} \). What is the pressure at \( 2.5 \, \text{m} \) height with speed \( 4.5 \, \text{m/s} \)? (\( \rho = 1000 \, \text{kg/m}^3 \), \( g = 9.8 \, \text{m/s}^2 \))

Q5. What is the absolute pressure at \( 300 \, \text{m} \) depth in seawater (\( \rho = 1.03 \times 10^3 \, \text{kg/m}^3 \)) with \( P_a = 1.01 \times 10^5 \, \text{Pa} \)? (Take \( g = 10 \, \text{m/s}^2 \))

Q6. A \( 40 \, \text{kg} \) wooden plank is placed on a performer’s chest. If each femur has an area of \( 12 \, \text{cm}^2 \), what is the pressure on the femurs? (Take \( g = 10 \, \text{m/s}^2 \))

Q7. What is the primary reason a heavy object falls faster than a lighter one through a viscous fluid?

Q8. A sphere of radius \( 0.03 \, \text{m} \) falls through machine oil (\( \eta = 0.113 \, \text{Pa s} \)) at \( 0.15 \, \text{m/s} \). What is the viscous drag force?

Q9. According to Pascal’s law, what happens to the pressure in a fluid when an external force is applied?

Q10. Why does a bubble collapse when the external pressure exceeds its internal pressure?

Q11. An aircraft (\( m = 2.2 \times 10^5 \, \text{kg} \), wing area \( 440 \, \text{m}^2 \)) flies level. What is the pressure difference across the wings? (Take \( g = 10 \, \text{m/s}^2 \))

Q12. A spray pump tube (\( 10 \, \text{cm}^2 \)) has 50 holes, each of diameter \( 0.8 \, \text{mm} \). If the flow speed inside is \( 1.2 \, \text{m/min} \), what is the ejection speed?

Q13. A hydraulic lift raises a \( 2300 \, \text{kg} \) load using a small piston of radius \( 5.0 \, \text{cm} \) and a large piston of radius \( 20 \, \text{cm} \). What force is applied on the small piston? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q14. A soap bubble of radius \( 11 \, \text{mm} \) has a surface tension of \( 0.027 \, \text{N/m} \). What is the excess pressure inside?

Q15. What does the equation of continuity imply about fluid flow in a pipe of varying cross-section?