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.
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Laminar Flow of an Incompressible Fluid in a Conduit With Arbitrary Cross Section, Arbitrary Time-Varying Pressure Gradient, and Arbitrary Initial Velocity
H. K. Hepworth,
H. K. Hepworth
Northern Arizona University, Flagstaff, Ariz.; Mechanical Engineering, Arizona State University, Tempe, Ariz.
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W. Rice
W. Rice
Mechanical Engineering, Arizona State University, Tempe, Ariz.
Search for other works by this author on:
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. Mar 1972, 94(1): 27-32 (6 pages)
Published Online: March 1, 1972
Article history
Received:
August 2, 1971
Online:
October 27, 2010
Citation
Hepworth, H. K., and Rice, W. (March 1, 1972). "Laminar Flow of an Incompressible Fluid in a Conduit With Arbitrary Cross Section, Arbitrary Time-Varying Pressure Gradient, and Arbitrary Initial Velocity." ASME. J. Basic Eng. March 1972; 94(1): 27–32. https://doi.org/10.1115/1.3425381
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