Laminar Flow of an Incompressible Fluid in a Conduit With Arbitrary Cross Section, Arbitrary Time-Varying Pressure Gradient, and Arbitrary Initial Velocity

[+] Author and Article Information
H. K. Hepworth

Northern Arizona University, Flagstaff, Ariz.; Mechanical Engineering, Arizona State University, Tempe, Ariz.

W. Rice

Mechanical Engineering, Arizona State University, Tempe, Ariz.

J. Basic Eng 94(1), 27-32 (Mar 01, 1972) (6 pages) doi:10.1115/1.3425381 History: Received August 02, 1971; Online October 27, 2010


A computer-oriented solution is given for the flow described in the title of the paper. The boundary shape is represented by specification of the coordinates of N points on the boundary; the initial velocity is represented by specification of L values of the velocity in the cross section at time zero; the arbitrary time-varying pressure gradient is implemented by use of Duhamel’s Theorem. In the solution method presented, boundary and initial conditions are satisfied in the least squares sense. The Gram determinant is used to determine eigenvalues and the Gram-Schmidt orthonormalizing procedure is used to construct a set of functions appropriate for a finite series solution. Computer programs are referenced which have been used to investigate the correctness of the solution and the accuracy obtainable with reasonable digital computational time.

Copyright © 1972 by ASME
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