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

1972 ◽  
Vol 94 (1) ◽  
pp. 27-32 ◽  
Author(s):  
H. K. Hepworth ◽  
W. Rice
Keyword(s):  
Pressure Gradient ◽  
Cross Section ◽  
Initial Velocity ◽  
Solution Method ◽  
Initial Conditions ◽  
Arbitrary Cross Section ◽  
Computational Time ◽  
Time Varying ◽  
Arbitrary Time ◽  
Gram Determinant

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.

Laminar Flow in an Annulus With Arbitrary Time-Varying Pressure Gradient and Arbitrary Initial Velocity

1969 ◽  
Vol 36 (2) ◽  
pp. 309-311 ◽  
Author(s):  
Satya Prakash
Keyword(s):  
Pressure Gradient ◽  
Initial Velocity ◽  
Hankel Transform ◽  
Initial Distribution ◽  
Circular Cylinders ◽  
Time Varying ◽  
Annular Space ◽  
Arbitrary Time ◽  
Constant Quantity ◽  
Finite Hankel Transform

In this paper, the problem of incompressible laminar viscous flow in the annular space bounded by two coaxial infinite circular cylinders with an arbitrary time-varying pressure gradient and with an arbitrary initial distribution of velocity has been studied. The present problem generalizes the several earlier works in which the pressure gradient and the initial distribution of velocity have been taken in special forms. The analysis has been made by the use of finite Hankel transform. The case of steady flow when the pressure gradient is constant has been deduced by taking the pressure gradient to be a constant quantity and then letting the time since the start of the motion be infinite. This result has been shown in agreement with the already well-established result.

Torsion of Composite Elastic Bars of Arbitrary Cross Section

1968 ◽  
Vol 90 (3) ◽  
pp. 435-440 ◽  
Author(s):  
E. M. Sparrow ◽  
H. S. Yu
Keyword(s):  
Exact Solution ◽  
Closed Form ◽  
Elastic Properties ◽  
Cross Section ◽  
Excellent Agreement ◽  
Solution Method ◽  
Circular Cross Section ◽  
High Accuracy ◽  
Arbitrary Cross Section ◽  
Closed Form Solutions

A method of analysis is presented for determining closed-form solutions for torsion of inhomogeneous prismatic bars of arbitrary cross section, the inhomogeneity stemming from the layering of materials of different elastic properties. It is demonstrated that the solution method is very easy to apply and provides results of high accuracy. As an application, solutions are obtained for the torsion of a bar of circular cross section consisting of two materials separated by a plane interface. The results are compared with those of various limiting cases and excellent agreement is found to exist. Among the limiting cases, an exact solution was derived by Green’s functions for the problem in which the interface between the materials coincides with a diameter of the circular cross section.

Magnetohydrodynamic pipe flow Part2. High Hartmann number

1962 ◽  
Vol 13 (4) ◽  
pp. 513-518 ◽  
Author(s):  
J. A. Shercliff
Keyword(s):  
Magnetic Fields ◽  
Pressure Gradient ◽  
Cross Section ◽  
Pipe Flow ◽  
Hartmann Number ◽  
Gradient Flow ◽  
Transverse Magnetic ◽  
Arbitrary Cross Section ◽  
Conducting Liquid ◽  
Experimental Pressure

The paper presents an improved, second approximation for the laminar motion of a conducting liquid at high Hartmann number in non-conducting pipes of arbitrary cross-section under uniform transverse magnetic fields. A satisfactory comparison with the author's previously experimental pressure gradient/flow results is made for the case of a circular pipe.

Pressure Distributions in Porous Ducts of Arbitrary Cross Section

1973 ◽  
Vol 95 (3) ◽  
pp. 342-348 ◽  
Author(s):  
J. C. P. Huang ◽  
H. S. Yu
Keyword(s):  
Pressure Gradient ◽  
Cross Section ◽  
Cross Sections ◽  
Porous Plate ◽  
Porous Wall ◽  
Design Criterion ◽  
Arbitrary Cross Section ◽  
Solid Particles ◽  
Equivalent Diameter ◽  
Pressure Distributions

A general analytical method has been developed to approximate the pressure distribution along a porous duct of an arbitrary cross section with uniform fluid extraction or addition through the wall. Application of this method is made to a variety of cross sections including circular tubes, parallel plate channels, elliptical ducts, rectangular ducts, annular ducts, and isosceles triangular ducts. Comparisons have been made with results from existing literature on cases of the circular porous tube and the parallel porous plate channel in which exact solutions are available. A numerical solution for the case of a parallel channel consisting of an impermeable wall on one side and a porous wall on the other side is also presented. One important filter duct design criterion has been found for each of the above cases. At a critical wall Reynolds number, defined by flow velocity normal to the wall and the equivalent diameter of the duct, the pressure gradient along the filter duct approaches zero. The zero pressure gradient in a filter duct ensures uniform filtration of solid particles.

Oscillating Flow in Ducts of Arbitrary Cross Section

1969 ◽  
Vol 73 (706) ◽  
pp. 894-896
Author(s):  
A. M. Abu-Sitta ◽  
D. G. Drake
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Pressure Gradient ◽  
Numerical Solution ◽  
Cross Section ◽  
Circular Cross Section ◽  
Arbitrary Cross Section ◽  
Oscillating Flow ◽  
Elliptic Case ◽  
Uniform Cross Section

The rectilinear flow of an incompressible viscous fluid along a duct of uniform cross section due to an oscillating pressure gradient has been considered by a number of investigators. The duct of circular cross .section has been treated by Richardson and Tyler and Sexl, the elliptic case by Khamrui, and the rectangular case by Drake and Fan and Chao. Recently Jeng has discussed the importance of this type of flow and has given a procedure for calculating a numerical solution for a duct of arbitrary cross-section. An interesting feature of these flows is that, at large frequencies when the flow is of boundary-layer type, the velocity at any instant has its maximum near the walls, the velocity overshooting its almost uniform distribution at the centre of the duct.

Flow in the Hydrodynamic Entrance Region of Ducts of Arbitrary Cross Section

1969 ◽  
Vol 91 (3) ◽  
pp. 345-354 ◽  
Author(s):  
David P. Fleming ◽  
E. M. Sparrow
Keyword(s):  
Experimental Data ◽  
Velocity Field ◽  
Pressure Drop ◽  
Cross Section ◽  
Cross Sections ◽  
Solution Method ◽  
Arbitrary Cross Section ◽  
Entrance Region ◽  
General Method ◽  
Good Agreement

A general method of analysis is presented for determining the developing velocity field and pressure drop for laminar flow in the entrance region of ducts having arbitrary cross sections. Application of the solution method is made to rectangular ducts and to triangular ducts. Available experimental data are compared with the analytical results and good agreement is found to prevail. Development characteristics for six ducts are brought together and compared, and various trends are identified.

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