Free Equation of Continuity MCQs with Answers

1. The equation of continuity for an incompressible fluid states that

• A. A1 v1 equals A2 v2, so the fluid speeds up where the pipe narrows
• B. A1 v1 equals A2 v2, so the fluid slows down where the pipe narrows
• C. the pressure is the same everywhere in the pipe
• D. the density changes along the pipe

Explanation: The same volume passes every cross section each second, so where the area falls the speed must rise in proportion. This is why a garden hose squirts further when a thumb covers part of the opening. The equation is simply the conservation of mass applied to a fluid of constant density.

2. Water flows through a pipe whose radius halves at a constriction. The speed of the water at the constriction becomes

• A. half
• B. double
• C. four times
• D. unchanged

Explanation: Area depends on the square of the radius, so halving the radius quarters the area, and by the continuity equation the speed must rise by a factor of four to carry the same volume per second. Answering double is the error of treating area as proportional to radius. This strong dependence is why small constrictions in a blood vessel raise flow speed so sharply.

3. Water flows at 2 m per second through a pipe of cross sectional area 0.02 m squared. The volume flow rate is

• A. 0.04 cubic metres per second
• B. 0.01 cubic metres per second
• C. 4 cubic metres per second
• D. 0.4 cubic metres per second

Explanation: Flow rate is area multiplied by speed, so 0.02 times 2 gives 0.04 cubic metres per second, that is 40 litres every second. Dividing rather than multiplying gives the 0.01 distractor. The same product appears on both sides of the continuity equation, which is why it is constant along a pipe.

4. An incompressible fluid flows through a pipe that becomes narrower in one section. The fluid speed increases in that region to maintain:

• A. Constant pressure
• B. Constant energy
• C. Constant mass flow rate
• D. Constant volume

Explanation: The same mass must pass every cross section each second, so where the area falls the speed must rise in proportion, which is the equation of continuity and is simply conservation of mass applied to a fluid. Pressure certainly does not stay constant; it falls in the constriction, which is Bernoulli's principle. This is why a thumb over a hose makes the water squirt further.