Two cylindrical pipes both carry an ideal fluid (zero viscosity) in laminar flow. Pipe A has radius R_A = 8 cm and flow velocity v_A = 2 cm/s. Pipe B has radius R_B = 4 cm and flow velocity v_B = 4 cm/s. Compared to the rate of flow in pipe A, that in pipe B is A) the same. B) half as large. C) twice as large. D) It depends on the length of the pipe.

Question

Quizplus · Accepted Answer

The rate of flow in a cylindrical pipe is given by the equation Q = πr^2v, where Q is the volume flow rate, r is the radius of the pipe, and v is the flow velocity. Since pipe B has a smaller radius than pipe A, but a larger flow velocity, the volume flow rate in pipe B is half as large as pipe A. Thus, the answer is B. The length of the pipe does not affect the answer, as long as laminar flow is maintained throughout the length of the pipe.

Two Cylindrical Pipes Both Carry an Ideal Fluid (Zero Viscosity)