NEET Mechanical Properties of Fluids — Set 19

Question 1

A bubble of radius $ 3 \, \text{mm} $ is blown at $ 30 \, \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 = 10 \, \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 10 \times 0.3 = 3000 \, \text{Pa} $. $ \frac{2 S}{r} = \frac{2 \times 0.0727}{3 \times 10^{-3}} = 48.47 \, \text{Pa} $. $ P_i = 1.01 \times 10^5 + 3000 + 48.47 = 1.04048 \times 10^5 \, \text{Pa} $.

Question 2

A pipe narrows from $ 0.07 \, \text{m}^2 $ to $ 0.035 \, \text{m}^2 $. If water flows at $ 2.4 \, \text{m/s} $ in the wider section, what is the speed in the narrower section?

Accepted Answer

Continuity equation: $ A_1 v_1 = A_2 v_2 $. $ A_1 = 0.07 \, \text{m}^2 $, $ v_1 = 2.4 \, \text{m/s} $, $ A_2 = 0.035 \, \text{m}^2 $. $ v_2 = \frac{A_1 v_1}{A_2} = \frac{0.07 \times 2.4}{0.035} = 4.8 \, \text{m/s} $.

Question 3

Which statement is incorrect regarding Torricelli’s law?

Accepted Answer

Torricelli’s law ($ v = \sqrt{2gh} $) assumes non-viscous flow and neglects losses, not depending on viscosity or requiring turbulence. The incorrect statement is that it depends on fluid viscosity.

NEET Physics: Mechanical Properties of Fluids — Practice Set 19

Q1. A bubble of radius \( 3 \, \text{mm} \) is blown at \( 30 \, \text{cm} \) depth in water (\( \rho = 1000 \, \text{kg/m}^3 \), \( S = 0.0727 \, \text{N/m} \)). What is the total pressure inside? (Take \( P_a = 1.01 \times 10^5 \, \text{Pa} \), \( g = 10 \, \text{m/s}^2 \))

Q2. A pipe narrows from \( 0.07 \, \text{m}^2 \) to \( 0.035 \, \text{m}^2 \). If water flows at \( 2.4 \, \text{m/s} \) in the wider section, what is the speed in the narrower section?

Q3. Which statement is incorrect regarding Torricelli’s law?

Q4. Why does a fluid’s flow rate remain constant in a pipe of varying diameter?

Q5. Why does a fluid’s viscosity contribute to energy loss in real flow systems?

Q6. What causes the height of capillary rise to be inversely proportional to the tube’s radius?

Q7. Why does blowing over a piece of paper lift it upwards?

Q8. Why does a fluid’s flow transition from streamline to turbulent beyond a critical speed?

Q9. Why does a liquid’s surface tension decrease with increasing temperature?

Q10. Why do fluids exert pressure only normal to a surface at rest?