NEET Mechanical Properties of Fluids — Set 6

Question 1

In streamline flow, why do streamlines never cross each other?

Accepted Answer

In streamline flow, each streamline represents the path of a fluid particle with a unique velocity at each point. If streamlines crossed, a particle at the intersection would have two different velocities simultaneously, which is impossible in steady flow.

Question 2

An aircraft ($ m = 3.5 \times 10^5 \, \text{kg} $, wing area $ 550 \, \text{m}^2 $) flies level. What is the pressure difference across the wings? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

$ \Delta P \cdot A = mg $. $ mg = 3.5 \times 10^5 \times 10 = 3.5 \times 10^6 \, \text{N} $, $ A = 550 \, \text{m}^2 $. $ \Delta P = \frac{3.5 \times 10^6}{550} = 6363.64 \, \text{Pa} \approx 6364 \, \text{Pa} $.

Question 3

A plate of area $ 0.08 \, \text{m}^2 $ moves at $ 0.4 \, \text{m/s} $ over a $ 0.25 \, \text{mm} $ thick oil film ($ \eta = 0.034 \, \text{Pa s} $). What force is required?

Accepted Answer

Viscous force: $ F = \eta \frac{v A}{l} $. $ \eta = 0.034 \, \text{Pa s} $, $ v = 0.4 \, \text{m/s} $, $ A = 0.08 \, \text{m}^2 $, $ l = 0.25 \times 10^{-3} \, \text{m} $. $ F = 0.034 \times \frac{0.4 \times 0.08}{0.25 \times 10^{-3}} = 0.034 \times 128 = 4.352 \, \text{N} $.

NEET Physics: Mechanical Properties of Fluids — Practice Set 6

Q1. In streamline flow, why do streamlines never cross each other?

Q2. An aircraft (\( m = 3.5 \times 10^5 \, \text{kg} \), wing area \( 550 \, \text{m}^2 \)) flies level. What is the pressure difference across the wings? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A plate of area \( 0.08 \, \text{m}^2 \) moves at \( 0.4 \, \text{m/s} \) over a \( 0.25 \, \text{mm} \) thick oil film (\( \eta = 0.034 \, \text{Pa s} \)). What force is required?

Q4. A soap film supports \( 4.0 \times 10^{-2} \, \text{N} \) over a \( 40 \, \text{cm} \) slider. What is the surface tension?

Q5. A sphere of radius \( 0.06 \, \text{m} \) moves at \( 0.13 \, \text{m/s} \) through glycerine (\( \eta = 0.83 \, \text{Pa s} \)). What is the viscous drag force?

Q6. What is the excess pressure inside a water drop of radius \( 1.8 \, \text{mm} \) at \( 20^\circ \text{C} \)? (Surface tension = \( 0.0727 \, \text{N/m} \))

Q7. A sphere of radius \( 0.02 \, \text{m} \) falls through glycerine (\( \eta = 0.83 \, \text{Pa s} \)) at a terminal velocity of \( 0.1 \, \text{m/s} \). What is the viscous drag force?

Q8. What is the reason a liquid’s terminal velocity depends on its radius when falling through a viscous medium?

Q9. Water flows at \( 2.6 \, \text{m/s} \) at \( 4.0 \, \text{m} \) height with pressure \( 1.7 \times 10^5 \, \text{Pa} \). What is the pressure at \( 2.0 \, \text{m} \) height with speed \( 3.8 \, \text{m/s} \)? (\( \rho = 1000 \, \text{kg/m}^3 \), \( g = 9.8 \, \text{m/s}^2 \))

Q10. A tank has a hole \( 1.1 \, \text{m} \) below the water surface, open to the atmosphere. What is the efflux speed? (Take \( g = 10 \, \text{m/s}^2 \))

Q11. What is the primary source of resistance to motion in a viscous fluid?

Q12. What causes the speed of efflux from a hole in a tank to equal the speed of a freely falling body from the same height?

Q13. What is the primary reason mercury does not wet glass?

Q14. What is the excess pressure inside an ethanol drop of radius \( 2.2 \, \text{mm} \) at \( 20^\circ \text{C} \)? (Surface tension = \( 0.0227 \, \text{N/m} \))

Q15. A pipe narrows from \( 0.12 \, \text{m}^2 \) to \( 0.04 \, \text{m}^2 \). If water flows at \( 1.6 \, \text{m/s} \) in the wider section, what is the speed in the narrower section?