Chapter 24, Problem 48P

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 $Q={\displaystyle {\int }_0^{R}2\pi rvdr}$,

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 $1/3$ rule to integrate.

(c) Find the percent error using the integral of the polynomial fit as the more correct value.