Concept explainers
Fully developed flow moving through a 40-cm diameter pipe has the following velocity profile:
Radius, r, cm | 0.0 | 2.5 | 5.0 | 7.5 | 10.0 | 12.5 | 15.0 | 17.5 | 20.0 |
Velocity, v, m/s | 0.914 | 0.890 | 0.847 | 0.795 | 0.719 | 0.543 | 0.427 | 0.204 | 0 |
Find the volume flow rate Q using the relationship
wherer is the radial axis of the pipe, R is the radius of the pipe, and v is the velocity. Solve the problem using two different approaches.
(a) Fit a polynomial curve to the velocity data and integrate analytically.
(b) Use multiple-application Simpson's
(c) Find the percent error using the
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Numerical Methods for Engineers
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