NEET Mechanical Properties of Fluids — Set 21

Question 1

Which of the following statements is correct about atmospheric pressure?

Accepted Answer

Atmospheric pressure decreases with altitude as the weight of the air column above reduces, a fundamental concept in the chapter’s discussion of pressure variation.

Question 2

What is the total pressure at a depth of $ 3.4 \, \text{m} $ in seawater ($ \rho = 1.03 \times 10^3 \, \text{kg/m}^3 $) with atmospheric pressure $ 1.01 \times 10^5 \, \text{Pa} $? (Take $ g = 9.8 \, \text{m/s}^2 $)

Accepted Answer

Total pressure: $ P = P_a + \rho g h $. $ P_a = 1.01 \times 10^5 \, \text{Pa} $, $ \rho = 1.03 \times 10^3 \, \text{kg/m}^3 $, $ g = 9.8 \, \text{m/s}^2 $, $ h = 3.4 \, \text{m} $. $ P = 1.01 \times 10^5 + 1.03 \times 10^3 \times 9.8 \times 3.4 = 1.01 \times 10^5 + 34319.6 = 1.353196 \times 10^5 \, \text{Pa} $.

Question 3

A spray tube ($ 10 \, \text{cm}^2 $) has 50 holes of diameter $ 0.9 \, \text{mm} $. If the flow speed is $ 2.5 \, \text{m/min} $, what is the ejection speed?

Accepted Answer

$ A_1 v_1 = A_2 v_2 $, $ v_1 = 2.5 \, \text{m/min} = 0.04167 \, \text{m/s} $, $ A_1 = 10 \times 10^{-4} \, \text{m}^2 $. Hole area: $ A_h = \pi (0.45 \times 10^{-3})^2 $, total $ A_2 = 50 \times \pi \times 2.025 \times 10^{-7} \approx 3.181 \times 10^{-5} \, \text{m}^2 $. $ v_2 = \frac{10 \times 10^{-4} \times 0.04167}{3.181 \times 10^{-5}} \approx 1.31 \, \text{m/s} $.

NEET Physics: Mechanical Properties of Fluids — Practice Set 21

Q1. Which of the following statements is correct about atmospheric pressure?

Q2. What is the total pressure at a depth of \( 3.4 \, \text{m} \) in seawater (\( \rho = 1.03 \times 10^3 \, \text{kg/m}^3 \)) with atmospheric pressure \( 1.01 \times 10^5 \, \text{Pa} \)? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q3. A spray tube (\( 10 \, \text{cm}^2 \)) has 50 holes of diameter \( 0.9 \, \text{mm} \). If the flow speed is \( 2.5 \, \text{m/min} \), what is the ejection speed?

Q4. Water flows through a horizontal pipe at a speed of \( 3 \, \text{m/s} \) with a pressure of \( 1.5 \times 10^5 \, \text{Pa} \). If the speed increases to \( 6 \, \text{m/s} \), what is the new pressure? (\( \rho = 1000 \, \text{kg/m}^3 \))

Q5. A container has whole blood (\( \rho = 1.06 \times 10^3 \, \text{kg/m}^3 \)) up to \( 1.5 \, \text{m} \). What is the gauge pressure at the bottom? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q6. Why does the pressure in a fluid decrease when its speed increases in a horizontal pipe?

Q7. A person stands on two bones, each with area \( 22 \, \text{cm}^2 \), exerting a total force of \( 588 \, \text{N} \). What is the average pressure on the bones?

Q8. What happens to the fluid velocity when a pipe narrows, assuming steady flow?

Q9. A \( 60 \, \text{kg} \) person stands on two bones, each with area \( 25 \, \text{cm}^2 \). What is the average pressure on the bones? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. A mercury barometer shows a height of \( 75 \, \text{cm} \) at sea level. What is the atmospheric pressure? (\( \rho = 13.6 \times 10^3 \, \text{kg/m}^3 \), \( g = 10 \, \text{m/s}^2 \))