Free Fluid Dynamics MCQs with Answers

1. A body falling through a fluid reaches terminal velocity when

• A. the drag force becomes zero
• B. the upward drag and upthrust together balance the weight, so the net force is zero
• C. the body stops moving completely
• D. gravity stops acting on the body

Explanation: Drag increases with speed, so the body accelerates until the retarding forces grow to match its weight, after which the acceleration is zero and the speed stays constant. The body is still moving, and gravity still acts; what has vanished is the resultant force, not any individual one. This is why a raindrop reaches the ground at a survivable speed rather than accelerating for its whole fall.

2. According to Stokes's law, the drag force on a small sphere moving slowly through a viscous fluid is proportional to

• A. the square of the speed
• B. the speed
• C. the cube of the radius
• D. the inverse of the radius

Explanation: Stokes's law gives the drag as 6 pi eta r v, so it rises in direct proportion to both the radius and the speed, provided the flow stays laminar. At higher speeds the flow becomes turbulent and drag grows roughly with the square of the speed instead. The law is what allows viscosity to be measured by timing a falling ball.

3. The terminal velocity of a small sphere falling through a viscous liquid is proportional to

• A. the radius of the sphere
• B. the square of the radius of the sphere
• C. the inverse of the radius
• D. the viscosity of the liquid

Explanation: Equating the weight less upthrust to the Stokes drag gives a terminal velocity proportional to r squared and inversely proportional to viscosity, so a sphere of twice the radius falls four times as fast. This is why fine dust hangs in the air for hours while a pebble drops at once. Raising the viscosity lowers the terminal velocity rather than raising it.

4. Flow is described as laminar when

• A. the fluid particles move in irregular, mixing paths
• B. each fluid particle follows the same smooth path as the one before it
• C. the fluid is at rest
• D. the fluid is compressible

Explanation: In laminar or streamline flow the layers slide over one another without mixing, so the velocity at any fixed point stays constant in time and streamlines never cross. Above a critical speed the motion breaks up into eddies and becomes turbulent, which dissipates far more energy. The Reynolds number is what predicts which regime a given flow is in.

5. 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.

6. 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.

7. Bernoulli's equation is essentially a statement of

• A. conservation of mass
• B. conservation of momentum
• C. conservation of energy for a flowing fluid
• D. Newton's third law

Explanation: The equation adds pressure energy, kinetic energy and potential energy per unit volume and states that the total is the same all along a streamline for steady, non viscous, incompressible flow. Conservation of mass is expressed separately by the continuity equation. The restriction to non viscous flow is why the equation only approximates real pipes.

8. According to Bernoulli's principle, where the speed of a fluid is high, its pressure is

• A. high
• B. low
• C. unchanged
• D. zero

Explanation: Since the total energy per unit volume is fixed, any gain in kinetic energy must be paid for by a fall in pressure energy. This is why a shower curtain is pulled inwards by the fast moving water stream and why two ships moving side by side are drawn together. The effect is easy to state and easy to misremember, so it is heavily tested.

9. The lift on an aeroplane wing arises because

• A. air moves faster over the curved upper surface, lowering the pressure there
• B. air moves faster under the wing
• C. the wing is lighter than air
• D. the engines push the wing upwards

Explanation: The aerofoil shape makes the air travel further and faster across the top, so by Bernoulli's principle the pressure above is lower than below and the difference multiplied by the wing area gives the lift. The wing also deflects air downwards, and by Newton's third law that contributes lift as well. Both descriptions are valid ways of accounting for the same force.

10. A Venturi meter measures the rate of flow of a fluid by using

• A. the temperature rise in a constriction
• B. the pressure difference between a wide section and a narrow section
• C. the weight of the fluid
• D. the colour change of the fluid

Explanation: The fluid speeds up in the throat, so its pressure falls, and measuring that pressure drop with a manometer gives the speed through the continuity and Bernoulli equations. Because it has no moving parts it is reliable and causes little permanent pressure loss. The same principle drives a carburettor and a filter pump.