NEET Mechanical Properties of Fluids — Set 18

Question 1

Which of the following statements is correct about streamline flow?

Accepted Answer

In streamline flow, fluid particles follow fixed paths (streamlines) with constant velocity at each point, occurring at low speeds where viscous forces dominate, not requiring high speed or turbulence.

Question 2

Which statement is incorrect about Bernoulli’s principle?

Accepted Answer

Bernoulli’s principle assumes non-viscous flow, not high viscosity, as viscosity causes energy loss, violating the energy conservation assumption. The incorrect statement is that it applies to highly viscous fluids.

Question 3

A fluid flows through a pipe with speeds $ v_1 = 2 \, \text{m/s} $ at height $ h_1 = 1 \, \text{m} $ and $ v_2 = 4 \, \text{m/s} $ at $ h_2 = 0 \, \text{m} $. If $ P_1 = 1.2 \times 10^5 \, \text{Pa} $, find $ P_2 $. ($ \rho = 1000 \, \text{kg/m}^3 $, $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Bernoulli’s equation: $ P_1 + \frac{1}{2} \rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho g h_2 $. $ P_1 = 1.2 \times 10^5 $, $ v_1 = 2 \, \text{m/s} $, $ h_1 = 1 \, \text{m} $, $ v_2 = 4 \, \text{m/s} $, $ h_2 = 0 \, \text{m} $. Left: $ 1.2 \times 10^5 + \frac{1}{2} \times 1000 \times 4 + 1000 \times 10 \times 1 = 1.2 \times 10^5 + 2000 + 10000 = 1.32 \times 10^5 $. Right: $ P_2 + \frac{1}{2} \times 1000 \times 16 = P_2 + 8000 $. $ 1.32 \times 10^5 = P_2 + 8000 $, $ P_2 = 1.24 \times 10^5 \, \text{Pa} $.

NEET Physics: Mechanical Properties of Fluids — Practice Set 18

Q1. Which of the following statements is correct about streamline flow?

Q2. Which statement is incorrect about Bernoulli’s principle?

Q3. A fluid flows through a pipe with speeds \( v_1 = 2 \, \text{m/s} \) at height \( h_1 = 1 \, \text{m} \) and \( v_2 = 4 \, \text{m/s} \) at \( h_2 = 0 \, \text{m} \). If \( P_1 = 1.2 \times 10^5 \, \text{Pa} \), find \( P_2 \). (\( \rho = 1000 \, \text{kg/m}^3 \), \( g = 10 \, \text{m/s}^2 \))

Q4. A tank has a hole \( 0.9 \, \text{m} \) below the water surface, open to the atmosphere. What is the efflux speed? (Take \( g = 10 \, \text{m/s}^2 \))

Q5. A hydraulic press applies \( 50 \, \text{N} \) on a piston of area \( 0.02 \, \text{m}^2 \). What force is exerted by a piston of area \( 0.1 \, \text{m}^2 \)?

Q6. Why does a liquid jet emerging from a small hole maintain a constant range until near the hole?

Q7. What is the force on a submarine window (\( 0.05 \, \text{m}^2 \)) at \( 600 \, \text{m} \) depth in seawater (\( \rho = 1.03 \times 10^3 \, \text{kg/m}^3 \)), interior at atmospheric pressure? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. A sphere of radius \( 0.025 \, \text{m} \) moves at \( 0.08 \, \text{m/s} \) through blood (\( \eta = 2.7 \times 10^{-3} \, \text{Pa s} \)). What is the viscous drag force?

Q9. An aircraft (\( m = 4.5 \times 10^5 \, \text{kg} \), 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. What determines whether a liquid wets a solid surface or forms droplets on it?