Answer: dP/dr = ρω²r.
- A dP/dr = ρω²r
- B dP/dr = ρv
- C dP/dr = -ρω²r
- D dP/dr = ρg
Correct answer: A. dP/dr = ρω²r
Explanation: In rotating fluid (centrifugal effect): the centripetal acceleration = ω²r. Pressure gradient provides this: dP/dr = ρω²r. Pressure increases outward.
Since the same volume of fluid must pass every cross-section per second (continuity), the fluid speeds up where the pipe narrows; Bernoulli's equation then says this faster-moving fluid has lower pressure - the principle behind a venturi meter and an aircraft wing's lift.
Concept context
Pressure, buoyancy, Bernoulli equation, viscosity, and surface tension.