NEET Mechanical Properties of Fluids — Set 15

Question 1

A pipe’s cross-sectional area decreases from $ 0.04 \, \text{m}^2 $ to $ 0.01 \, \text{m}^2 $. If the speed at the larger end is $ 2.5 \, \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 = 0.04 \, \text{m}^2 $, $ v_1 = 2.5 \, \text{m/s} $, $ A_2 = 0.01 \, \text{m}^2 $. $ v_2 = \frac{A_1 v_1}{A_2} = \frac{0.04 \times 2.5}{0.01} = 10 \, \text{m/s} $.

Question 2

A bubble of radius $ 3.5 \, \text{mm} $ is blown at $ 15 \, \text{cm} $ depth in water ($ \rho = 1000 \, \text{kg/m}^3 $, $ S = 0.0727 \, \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 $)

Accepted Answer

$ P_i = P_a + \rho g h + \frac{2 S}{r} $. $ P_a = 1.01 \times 10^5 \, \text{Pa} $, $ \rho g h = 1000 \times 9.8 \times 0.15 = 1470 \, \text{Pa} $. $ \frac{2 S}{r} = \frac{2 \times 0.0727}{3.5 \times 10^{-3}} = 41.54 \, \text{Pa} $. $ P_i = 1.01 \times 10^5 + 1470 + 41.54 = 1.02471 \times 10^5 \, \text{Pa} $.

Question 3

A soap bubble of radius $ 8 \, \text{mm} $ has a surface tension of $ 0.027 \, \text{N/m} $. What is the excess pressure inside?

Accepted Answer

Excess pressure in a bubble: $ \Delta P = \frac{4 S}{r} $. $ S = 0.027 \, \text{N/m} $, $ r = 8 \times 10^{-3} \, \text{m} $. $ \Delta P = \frac{4 \times 0.027}{8 \times 10^{-3}} = 13.5 \, \text{Pa} $.

NEET Physics: Mechanical Properties of Fluids — Practice Set 15

Q1. A pipe’s cross-sectional area decreases from \( 0.04 \, \text{m}^2 \) to \( 0.01 \, \text{m}^2 \). If the speed at the larger end is \( 2.5 \, \text{m/s} \), what is the speed at the smaller end?

Q2. A bubble of radius \( 3.5 \, \text{mm} \) is blown at \( 15 \, \text{cm} \) depth in water (\( \rho = 1000 \, \text{kg/m}^3 \), \( S = 0.0727 \, \text{N/m} \)). What is the total pressure inside? (Take \( P_a = 1.01 \times 10^5 \, \text{Pa} \), \( g = 9.8 \, \text{m/s}^2 \))

Q3. A soap bubble of radius \( 8 \, \text{mm} \) has a surface tension of \( 0.027 \, \text{N/m} \). What is the excess pressure inside?

Q4. The pressure at a depth of \( 3 \, \text{m} \) in ethyl alcohol (\( \rho = 806 \, \text{kg/m}^3 \)) is measured with atmospheric pressure as \( 1.01 \times 10^5 \, \text{Pa} \). What is the total pressure? (Take \( g = 10 \, \text{m/s}^2 \))

Q5. A \( 70 \, \text{kg} \) person stands on two bones, each with area \( 16 \, \text{cm}^2 \). What is the average pressure on the bones? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q6. A metal plate of area \( 0.05 \, \text{m}^2 \) moves over a liquid film (\( \eta = 0.02 \, \text{Pa s} \)) of thickness \( 0.2 \, \text{mm} \) at \( 0.5 \, \text{m/s} \). What is the force required?

Q7. Water flows at \( 1.5 \, \text{m/s} \) at \( 2.5 \, \text{m} \) height with pressure \( 1.8 \times 10^5 \, \text{Pa} \). What is the pressure at \( 0.5 \, \text{m} \) height with speed \( 2.5 \, \text{m/s} \)? (\( \rho = 1000 \, \text{kg/m}^3 \), \( g = 10 \, \text{m/s}^2 \))

Q8. A soap film on a wire supports \( 1.2 \times 10^{-2} \, \text{N} \) over a \( 25 \, \text{cm} \) slider. What is the surface tension?

Q9. An aircraft (\( m = 4.0 \times 10^5 \, \text{kg} \), wing area \( 600 \, \text{m}^2 \)) flies level. What is the pressure difference across the wings? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q10. Which statement is incorrect about hydrostatic pressure?