NEET Mechanical Properties of Fluids — Set 7

Question 1

What is the key assumption behind the equation of continuity for fluid flow?

Accepted Answer

The equation of continuity ($ A v = \text{constant} $) assumes the fluid is incompressible, meaning its density remains constant, ensuring mass conservation in steady flow through varying cross-sections.

Question 2

A cylindrical vessel is filled with water ($ \rho = 1000 \, \text{kg/m}^3 $) to a height of $ 2 \, \text{m} $. What is the pressure at the bottom of the vessel if the atmospheric pressure is $ 1.01 \times 10^5 \, \text{Pa} $? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Using the pressure variation with depth: $ P = P_a + \rho g h $. Given: $ P_a = 1.01 \times 10^5 \, \text{Pa} $, $ \rho = 1000 \, \text{kg/m}^3 $, $ g = 10 \, \text{m/s}^2 $, $ h = 2 \, \text{m} $. $ P = 1.01 \times 10^5 + 1000 \times 10 \times 2 $. $ P = 1.01 \times 10^5 + 20000 = 1.21 \times 10^5 \, \text{Pa} $.

Question 3

A tank has a hole $ 0.7 \, \text{m} $ below the water surface, open to the atmosphere. What is the efflux speed? (Take $ g = 9.8 \, \text{m/s}^2 $)

Accepted Answer

Torricelli’s law: $ v = \sqrt{2 g h} $. $ g = 9.8 \, \text{m/s}^2 $, $ h = 0.7 \, \text{m} $. $ v = \sqrt{2 \times 9.8 \times 0.7} = \sqrt{13.72} \approx 3.7 \, \text{m/s} $.

NEET Physics: Mechanical Properties of Fluids — Practice Set 7

Q1. What is the key assumption behind the equation of continuity for fluid flow?

Q2. A cylindrical vessel is filled with water (\( \rho = 1000 \, \text{kg/m}^3 \)) to a height of \( 2 \, \text{m} \). What is the pressure at the bottom of the vessel if the atmospheric pressure is \( 1.01 \times 10^5 \, \text{Pa} \)? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A tank has a hole \( 0.7 \, \text{m} \) below the water surface, open to the atmosphere. What is the efflux speed? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q4. A hydraulic lift has a small piston of area \( 0.01 \, \text{m}^2 \) and a large piston of area \( 0.09 \, \text{m}^2 \). If a force of \( 100 \, \text{N} \) is applied on the small piston, what is the force exerted by the large piston?

Q5. What is the primary condition for streamline flow to occur in a fluid?

Q6. An aircraft (\( m = 2.5 \times 10^5 \, \text{kg} \), wing area \( 400 \, \text{m}^2 \)) flies at \( 900 \, \text{km/h} \). What is the pressure difference across the wings? (Take \( g = 10 \, \text{m/s}^2 \), \( \rho_{\text{air}} = 1.2 \, \text{kg/m}^3 \))

Q7. Water flows at \( 2.5 \, \text{m/s} \) at \( 3 \, \text{m} \) height with pressure \( 1.5 \times 10^5 \, \text{Pa} \). What is the pressure at \( 1 \, \text{m} \) height with speed \( 3.5 \, \text{m/s} \)? (\( \rho = 1000 \, \text{kg/m}^3 \), \( g = 9.8 \, \text{m/s}^2 \))

Q8. What is the total pressure at a depth of \( 1.6 \, \text{m} \) in air (\( \rho = 1.29 \, \text{kg/m}^3 \)) with atmospheric pressure \( 1.01 \times 10^5 \, \text{Pa} \)? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q9. A soap film supports \( 2.4 \times 10^{-2} \, \text{N} \) over a \( 48 \, \text{cm} \) slider. What is the surface tension?

Q10. A sphere of radius \( 0.035 \, \text{m} \) moves at \( 0.09 \, \text{m/s} \) through glycerine (\( \eta = 0.83 \, \text{Pa s} \)). What is the viscous drag force?

Q11. A manometer with ethyl alcohol (\( \rho = 806 \, \text{kg/m}^3 \)) shows a height difference of \( 0.3 \, \text{m} \). What is the pressure difference? (Take \( g = 10 \, \text{m/s}^2 \))

Q12. What is the force on a submarine window (\( 0.07 \, \text{m}^2 \)) at \( 350 \, \text{m} \) depth in seawater (\( \rho = 1.03 \times 10^3 \, \text{kg/m}^3 \)), interior at atmospheric pressure? (Take \( g = 10 \, \text{m/s}^2 \))

Q13. A capillary tube of radius \( 0.65 \, \text{mm} \) 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 \( g = 9.8 \, \text{m/s}^2 \))

Q14. What is the main reason a plane’s wings generate lift during flight?

Q15. A sphere of radius \( 0.045 \, \text{m} \) moves at \( 0.15 \, \text{m/s} \) through machine oil (\( \eta = 0.034 \, \text{Pa s} \)). What is the viscous drag force?