To measure the mass flow rate of a fluid in a laminar flow through a circular pipe, a hot wire type velocity meter is placed in the center of the pipe. Assuming that the measuring station is far from the entrance of the pipe, the velocity distribution is parabolic, or

where Umax is the centerline velocity (r = 0)r is the radial distance from the pipe centerlineD is the pipe diameter.(a) Derive an expression for the average fluid velocity at the cross-section.(b) Obtain an expression for the mass flow rate.(c) If the fluid is mercury at 30?C, D = 10 cm, and the measured value of Umax is 0.2 cm/s, calculate the mass flow rate from the measurement.GIVENFully developed flow of mercury through a circular pipeParabolic velocity distribution: u(r)/Umax = 1 ?? (2r/D)2Mercury temperature (T) = 30?CPipe diameter (D) = 10 cm = 0.1 mMeasured center velocity (Umax) = 0.2 cm/s = 0.002m/s

Transcribed Image Text:

2r - [-) u(r) U. mux