An incompressible ideal fluid flows steadily through a pipe that has a change in diameter. The fluid speed at a location where the pipe diameter is 8.0 cm is 1.28 m/s . What is the fluid speed at a location where the diameter has narrowed to 4.0 cm?
A) 5.1 m/s
B) 2.6 m/s
C) 0.32 m/s
D) 0.64 m/s
E) 1.3 m/s

Question

An incompressible ideal fluid flows steadily through a pipe that has a change in diameter. The fluid speed at a location where the pipe diameter is  8.0 cm  is  1.28 m/s . What is the fluid speed at a location where the diameter has narrowed to  4.0 cm?
A)  5.1 m/s
B)  2.6 m/s
C)  0.32 m/s 
D)  0.64 m/s
E)  1.3 m/s

Quizplus · Accepted Answer

The fluid speed increases as the pipe diameter decreases due to the conservation of mass principle, which can be mathematically described by the equation A1V1 = A2V2, where A1 and A2 are the cross-sectional areas of the pipe at the two locations, and V1 and V2 are the fluid speeds at these locations. Given the diameters, the area ratio is (8.0 cm / 4.0 cm)^2 = 4, so V2 = 4 * 1.28 m/s = 5.12 m/s, which is closest to 5.1 m/s.

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