Questions: Bernoulli's Equation

Question 1

Water flows through a pipe that narrows from a large diameter to a small diameter. According to Bernoulli's equation, what happens to the static pressure in the narrow section?

• A. It increases, because the water is more compressed
• B. It stays the same, because mass is conserved
• C. It decreases, because velocity increases and total energy is constant
• D. It increases, because more fluid passes through per second

Answer: (C)

By the continuity equation, flow speed must increase in the narrower section to conserve mass. Bernoulli's equation then requires that an increase in the kinetic energy term (½ρV²) must be offset by a decrease in the pressure term P (assuming constant elevation). This is the classic venturi effect: faster flow, lower static pressure. Options A and D reflect common intuitions about compression and flow rate that do not apply to incompressible flow.

Question 2

Bernoulli's equation can be used to calculate pressure losses in a long pipe with significant friction.

• T. True
• F. False

Answer: False

Bernoulli's equation applies only to inviscid (frictionless) flow. In a real pipe, viscous friction dissipates mechanical energy as heat, so the total head is not conserved. For real pipe flow you must use the full energy equation, which includes a head loss term (h_L) accounting for friction and minor losses. Using Bernoulli's equation on a frictional system will overestimate downstream pressure.

Question 3

State the four key assumptions that must hold for Bernoulli's equation to be valid.

Model answer: The flow must be (1) steady (not changing with time), (2) incompressible (constant density), (3) inviscid (no viscous friction), and (4) applied along a single streamline.

Each assumption eliminates a term or effect that would otherwise appear in the more general energy equation. Unsteady flow adds a time-derivative term; compressible flow changes density; viscosity introduces energy dissipation; and applying the equation across streamlines is invalid in rotational flow where the Bernoulli constant differs between streamlines. Checking these assumptions is the first step before applying the equation to any problem.