By Dr. A. C. Thompson

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Additional resources for Basic Hydrodynamics

Example text

0 Δψ. The frictional force is given by the difference in shear stress τ on the top and bottom faces times the area of these faces. 0 X Ax if the flow is nearly parallel to the x-direction as assumed for the boundary layer. 0 X Δψ/ Uh K. 0 X Ay]+1/2, K if the steps are small. The momentum equation thus becomes This can be written So that if τ can be related to U, downstream values of U can be calculated from a known set of upstream values. The solution for the whole boundary layer can be found by 'marching' downstream.

The stream function SP and potential PP are calculated from the potential flow functions for a source q q ψ = — θ, ψ = — In r 2jt 2jt (3) In lines 230 to 260 the stream function and velocity potential are printed and an option is given to repeat the calculation for a further point. The program stops at line 270. 2 Splot: streamlines of sources and a stream A program, SPLOT, for finding the streamlines due to a stream and a number of sources (or sinks), follows. The program finds the value of stream function ψ at points on a grid and then finds the height at which a given value of ψ occurs on each column of the grid.

This can be one of a number of principles classed as variational or as weighted residual methods. The briefest explanation for potentialflowsis provided by a variational principle. One possible principle is that the solution must be one in which the energy of the flow is a minimum. For incompressible flow, strain energy cannot be stored so we find a flow with minimum kinetic energy (this being the only part of the total energy which can change).