By Dr. A. C. Thompson
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E. 23) where μ = viscosity of fluid. 34 Potential flow fundamentals The definition of ψ can also be used to give Δ Δψ »·-- ( ί / ι κ „ + ί ,,,)/2 <"4> Finally, for a flat plate parallel to a stream the velocity at the edge of the layer is always t/0, so by Bernoulli's equation p is constant and dpi(dx = 0. This gives an equation for the velocity μΑχ t W - ^,κ + ^—22 (U2*. K+i + Ϊ/2!. 25. The process can then be repeated to 'march' downstream. 99 U0 v = kinematic viscosity of fluid. 18. 13 Bibliography 1.
0 CIRCULATION G/2PI? 564609027 TYPE Y TO RECALCULATE V- N 43 44 Potential flow fundamentals Program notes (1) The dimension statement in line 100 sets up arrays for up to 100 points on the transformed shape. The x and y coordinates are stored in X2(100) and Y2(100), the velocity potential in P2(100) and the velocity in V2(100). (2) Lines 110 to 140 input data on the circle to be transformed. The radius, RC, x and y-coordinates of the centre, XC, YC, and the number of points on the surface, NP, are called for.
At line 1100 the routine returns to line 160. (8) Subroutine 2000 plots the new shape. Scale factor SF, jc-offset XS and y-offset YS are input in lines 2010 to 2030. Lines 2040 to 2050 set up the screen for plotting. In lines 2060 to 2240 the points are plotted. Each x and y value is scaled and offset to fit in the 360 X 160 picture space, in lines 2070 to 2080. The first point is selected by line 2090 and plotted as a single dot in line 2200. 19 Velocities and pressures on a wing shape Worked examples 45 points are joined by lines from the last point in lines 2100 and 2110.