A long, smooth pipe carrying an ideal liquid gradually narrows so that its…
PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids
Problem
A long, smooth pipe carrying an ideal liquid gradually narrows so that its cross-sectional area at one location is exactly half the area at a point farther upstream. No elevation change occurs along this segment.
(a) Qualitatively describe how the liquid’s speed and pressure change as it moves from the wider region into the narrower region. Your explanation should refer to fundamental conservation principles.
(b) Suppose the pipe instead narrows so that its radius decreases by a factor of three. By what factor does the liquid’s speed change between the two locations? Show your reasoning clearly.
(c) Explain why your answer to part (b) would remain valid even if the liquid were oil rather than water, provided the oil can still be treated as incompressible.