Q: Water enters a pipe of cross-section 4\text{ cm}^2 at 2\text{ m/s} and leaves through a section of area 2\text{ cm}^2. The exit speed is:

4\text{ m/s}. A_1 v_1 = A_2 v_2 \Rightarrow 4 \times 2 = 2 \times v_2 \Rightarrow v_2 = 4\text{ m/s}.

Q: Water flows at 0.02\text{ m}^3/\text{s} through a pipe of cross-sectional area 0.01\text{ m}^2. The speed of flow is:

2\text{ m/s}. v = \dfrac{Q}{A} = \dfrac{0.02}{0.01} = 2\text{ m/s}.

Question 1

The equation of continuity for the steady flow of an incompressible fluid, A_1 v_1 = A_2 v_2, is a direct consequence of the conservation of:

Accepted Answer

Mass. In steady flow the mass entering any section per second must equal the mass leaving it, giving \rho A v =  constant. For an incompressible fluid \rho cancels, leaving Av =  constant.

Question 2

Water flows through a pipe whose cross-sectional area is halved at a constriction. The speed of flow at the constriction:

Accepted Answer

Doubles. By continuity Av =  constant, so v \propto \dfrac{1}{A}. Halving the area doubles the speed.

Question 3

The diameter of a pipe is reduced to half at a narrow section. The speed of the liquid at that section becomes:

Accepted Answer

4 times. Area \propto d^2, so halving the diameter reduces the area to one-fourth. Since v \propto \dfrac{1}{A}, the speed becomes 4 times.

Question 4

Water enters a pipe of cross-section 4	ext{ cm}^2 at 2	ext{ m/s} and leaves through a section of area 2	ext{ cm}^2. The exit speed is:

Accepted Answer

4	ext{ m/s}. A_1 v_1 = A_2 v_2 \Rightarrow 4 	imes 2 = 2 	imes v_2 \Rightarrow v_2 = 4	ext{ m/s}.

Question 5

The volume flow rate of a liquid of speed v through a pipe of cross-sectional area A is given by:

Accepted Answer

Av. In one second the liquid advances a distance v, sweeping out a cylinder of volume Av. Its SI unit is 	ext{m}^3/	ext{s}.

Question 6

Water flows at 0.02	ext{ m}^3/	ext{s} through a pipe of cross-sectional area 0.01	ext{ m}^2. The speed of flow is:

Accepted Answer

2	ext{ m/s}. v = \dfrac{Q}{A} = \dfrac{0.02}{0.01} = 2	ext{ m/s}.

Question 7

Water flows through two sections of a pipe whose radii are in the ratio 1 : 2. The ratio of the flow speeds at those sections is:

Accepted Answer

4 : 1. Area \propto r^2, so the areas are in the ratio 1 : 4. Since v \propto \dfrac{1}{A}, the speeds are in the ratio 4 : 1 — fastest in the narrow section.

Question 8

A streamline in a flowing fluid is defined as a curve such that:

Accepted Answer

The tangent at every point gives the direction of fluid velocity there. By construction, the velocity vector of the fluid element at a point is tangential to the streamline passing through that point.

Question 9

Two streamlines in a steady flow can never intersect because:

Accepted Answer

The fluid would then need two different velocities at the same point. At an intersection the tangent — and hence the velocity — would be ambiguous. Since a fluid element has one definite velocity at a point in steady flow, streamlines cannot cross.

Question 10

The flow of a liquid through a pipe is regarded as turbulent if the Reynolds number R_e is:

Accepted Answer

Greater than 2000. Flow is laminar for R_e < 1000, unstable in the transition band 1000 < R_e < 2000, and fully turbulent for R_e > 2000.

Question 11

The Reynolds number for a fluid of density \rho and viscosity \eta flowing with speed v through a tube of diameter D is:

Accepted Answer

\dfrac{\rho v D}{\eta}. R_e = \dfrac{\rho v D}{\eta} compares inertial to viscous forces. It is a pure number with no units.

Question 12

The Reynolds number is a:

Accepted Answer

Dimensionless quantity. It is the ratio of inertial force to viscous force, so all dimensions cancel and it is a pure number.

Question 13

The critical velocity of a liquid flowing through a tube is the speed:

Accepted Answer

Above which streamline flow changes to turbulent flow. Below the critical velocity the flow is orderly and laminar; above it the flow breaks into eddies and becomes turbulent.

Question 14

The mass flow rate of a fluid of density \rho through a pipe of area A at speed v is:

Accepted Answer

ho A v. Volume flow rate is Av, so the mass crossing a section per second is ho Av, measured in 	ext{kg/s}.

Question 15

Water emerges faster when the nozzle of a garden hose is partially closed with a thumb because:

Accepted Answer

Reducing the area increases the speed, by the equation of continuity. The same volume per second must pass through a smaller opening, so Av =  constant forces the exit speed up.

Question 16

In the steady flow of an incompressible liquid, the product Av along a tube of flow is:

Accepted Answer

Constant at every cross-section. That is precisely the statement of the equation of continuity: the volume flow rate is the same through every section of the tube of flow.

Question 17

Water enters a pipe of area 6	ext{ cm}^2 at 3	ext{ m/s} and leaves through a section of area 2	ext{ cm}^2. The exit speed is:

Accepted Answer

9	ext{ m/s}. A_1v_1 = A_2v_2 \Rightarrow 6 	imes 3 = 2 	imes v_2 \Rightarrow v_2 = 9	ext{ m/s}.

Question 18

Water flows at a rate of 0.05	ext{ m}^3/	ext{s} through a pipe of cross-sectional area 0.005	ext{ m}^2. The flow speed is:

Accepted Answer

10	ext{ m/s}. v = \dfrac{Q}{A} = \dfrac{0.05}{0.005} = 10	ext{ m/s}.

Question 19

Water flowing at 1	ext{ m/s} in a pipe of diameter 4	ext{ cm} enters a narrow section of diameter 2	ext{ cm}. The speed in the narrow section is:

Accepted Answer

4	ext{ m/s}. Area \propto d^2, so the area falls to one-fourth and the speed rises four times: v_2 = 4	ext{ m/s}.

Question 20

Two sections of a pipe have radii in the ratio 2 : 3. The ratio of the flow speeds in them is:

Accepted Answer

9 : 4. Areas are in the ratio 4 : 9, and since v \propto \dfrac{1}{A}, the speeds are in the ratio 9 : 4.

Continuity Equation — MH-CET Physics MCQs with Solutions

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