Free Bernoulli's Equation MCQs with Answers

1. 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.

2. 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.

3. 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.

4. 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.

5. Blood pressure measured in a major artery is highest

• A. where the artery is narrowest
• B. where the blood flows fastest
• C. where the vessel is widest and the blood moves slowest
• D. at the capillaries

Explanation: Bernoulli's principle applies inside the body as well: where the cross section is large the speed is low and more of the energy remains as pressure. Where a vessel narrows, the blood accelerates and the lateral pressure on the wall falls. This is one reason an aneurysm, a widened weak spot, experiences a higher pressure and tends to grow.

6. In streamline flow through a horizontal pipe of uniform cross section, Bernoulli's equation predicts that the pressure

• A. rises steadily along the pipe
• B. stays the same along the pipe for an ideal fluid
• C. falls to zero at the outlet
• D. depends on the colour of the pipe

Explanation: With constant area the speed is constant by continuity, and with no height change the potential term is constant too, so the pressure term must also be constant for an ideal fluid. Real fluids do lose pressure along such a pipe because viscosity dissipates energy, which is exactly the effect Bernoulli's equation leaves out. Comparing the ideal prediction with the real behaviour is how the role of viscosity is demonstrated.

7. A spinning cricket ball swings in flight because

• A. gravity acts sideways on a spinning body
• B. the spin makes the ball lighter
• C. air moves faster on one side of the ball, creating a pressure difference across it
• D. the ball changes shape in the air

Explanation: The spinning surface drags air round with it, so the airflow is faster on one side and slower on the other, and by Bernoulli's principle the resulting pressure difference pushes the ball sideways. This sideways force on a spinning body is the Magnus effect, and it is why a swing bowler polishes one side of the ball. The same physics curves a football and lifts a golf ball.

8. In a pipe of varying cross-section, as fluid enters the narrower region it exhibits:

• A. High velocity, high pressure
• B. High velocity, low pressure
• C. Low velocity, high pressure
• D. Low velocity, low pressure

Explanation: Continuity forces the speed up in the constriction, and since the total energy per unit volume is fixed, the gain in kinetic energy must be paid for by a drop in pressure energy. This pairing of fast flow with low pressure is the heart of Bernoulli's principle. A Venturi meter measures flow rate by reading exactly this pressure difference.

9. The curved shape of an airplane wing causes air to move faster over the top surface. This leads to:

• A. Greater pressure on the top
• B. Lower pressure on the top
• C. Equal pressure on both sides
• D. Zero pressure above the wing

Explanation: Faster flow means lower pressure by Bernoulli's principle, so the pressure above the wing falls below that underneath and the difference multiplied by the wing area provides the lift. The wing also deflects air downwards, and by Newton's third law that contributes lift as well, so both descriptions account for the same force. The pressure above never reaches zero.