Fluid Dynamics

Practice Questions:

Question 21: easy

Assertion (A): In streamline flow streamlines never intersect each other.

Reason (R): If streamline intersect then their must two velocities of fluid particle at the point of intersection, which is impossible.

1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (3) (A) is true but (R) is false

4. (4) Both (A) and (R) are false

View Answer

Assertion (A) is true by definition of streamline flow.

Reason (R) is true because intersection would imply multiple velocity vectors at a single point, which is physically impossible.

(R) correctly explains (A).

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Question 22: easy

Assertion (A): The stream of water emerging from a water tap “necks down” as it falls.

Reason (R): The volume flow rate at different levels is same.

1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (3) (A) is true but (R) is false

4. (4) Both (A) and (R) are false

View Answer

Concept: Continuity equation for fluid flow. For an incompressible fluid in steady flow, the volume flow rate $AV$ (Area × Velocity) must remain constant. As water falls, its velocity $V$ increases due to gravity, therefore, its cross-sectional area $A$ must decrease, causing it to 'neck down'. Both Assertion and Reason are true, and Reason is the correct explanation for Assertion.

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Question 23: easy

The viscous drag acting on a metal sphere of diameter $1 \text{mm}$, falling through a fluid of viscosity $0.8 \text{Pa} \text{s}$ with a velocity of $2 \text{m} \text{s}^{-1}$ is equal to

1. $1.5 \times 10^{-3} \text{N}$

2. $20 \times 10^{-3} \text{N}$

3. $15 \times 10^{-3} \text{N}$

4. $30 \times 10^{-3} \text{N}$

View Answer

Using Stokes' Law: $F = 6\pi\eta r v$. Here, $r = 0.5 \times 10^{-3} \text{m}$, $\eta = 0.8 \text{Pa} \text{s}$, and $v = 2 \text{m/s}$. $F = 6 \times \pi \times 0.8 \times 0.5 \times 10^{-3} \times 2 \approx 15 \times 10^{-3} \text{N}$.

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Question 24: moderate

A small hole of area of cross-section $2 \text{ mm}^2$ is present near the bottom of a fully filled open tank of height $2 \text{ m}$. Taking $g = 10 \text{ m/s}^2$, the rate of flow of water through the open hole would be nearly

(2019)

1. $12.6 \times 10^{-6} \text{ m}^3/\text{s}$

2. $8.9 \times 10^{-6} \text{ m}^3/\text{s}$

3. $2.23 \times 10^{-6} \text{ m}^3/\text{s}$

4. $6.4 \times 10^{-6} \text{ m}^3/\text{s}$

View Answer

Velocity of efflux is $v = \sqrt{2gh} = \sqrt{2 \times 10 \times 2} = \sqrt{40} \text{ m/s}$. The rate of flow is given by $Q = Av = 2 \times 10^{-6} \times \sqrt{40} \approx 12.64 \times 10^{-6} \text{ m}^3/\text{s}$.

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Question 25: moderate

A wind with speed $40 \text{ m/s}$ blows parallel to the roof of a house. The area of the roof is $250 \text{ m}^2$. Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be ($P_{air} = 1.2 \text{ kg/m}^3$):

(2015)

1. $4.8 \times 10^5 \text{ N}$, upwards

2. $2.4 \times 10^5 \text{ N}$, upwards

3. $2.4 \times 10^5 \text{ N}$, downwards

4. $4.8 \times 10^5 \text{ N}$, downwards

View Answer

By Bernoulli's theorem, the pressure difference is $\Delta P = \frac{1}{2}\rho v^2 = \frac{1}{2} \times 1.2 \times (40)^2 = 960 \text{ N/m}^2$. The upward force is $F = \Delta P \times A = 960 \times 250 = 2.4 \times 10^5 \text{ N}$ directed upwards.

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