The equation of continuity for an incompressible fluid states that
Correct answer: A. A1 v1 equals A2 v2, so the fluid speeds up where the pipe narrows
- 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.
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About Equation of Continuity
The equation of continuity expresses conservation of mass in fluid flow. For steady incompressible flow, Av remains constant, so fluid speed increases when the cross-sectional area decreases; for compressible flow, ρAv is constant. This relation describes flow rate and area-speed changes without including pressure effects from Bernoulli’s equation.
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