Fit a polynomial curve to the noncore data and integrate

Reference no: EM131064810

Fully developed flow of a Bingham plastic fluid moving through a 12-in diameter pipe has the given velocity profile. The flow of a Bingham fluid does not shear the center core, producing plug flow in the region around the centerline.

Radius, r, in	0	1	2	3	4	5	6
Velocity, v, ft/s	5.00	5.00	4.62	4.01	3.42	1.69	0.00

Find the total volume flow rate Q using the relationship Q = _r1∫^r2 2prv dr + v_c A_c, where r is the radial axis of the pipe, v is the velocity, v_c is the velocity at the core, and Ac is the cross sectional area of the plug. Solve the problem using two different approaches.

(a) Fit a polynomial curve to the noncore data and integrate.

(b) Use multiple-application Simpson's rule to integrate.

Reference no: EM131064810

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