Question: Fully developed flow moving through a 40-cm diameter pipe has the following velocity profile:
Find the volume flow rate Q using the relationship Q = ?^?R0 2I?rI? dr, where r is the radial axis of the pipe, R is the radius of the pipe, and I? is the velocity. Solve the problem using two different approaches.
(a) Fit a polynomial carve to the velocity data and integrate analytically.
(b) Use multiple-application Simpson's 1/3 rule to integrate.
(c) Find the percent error using the integral of the polynomial fit as the more correctvalue.