# Basic Hydrodynamics by Dr. A. C. Thompson

By Dr. A. C. Thompson

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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. (3) At line 145 a message to indicate that the program is continuing is printed. (4) At line 150 the transformation subroutine is called and after this, in lines 160 to 210, the xy y coordinates of points on the new shape are printed.

463505574 READY TO PLOT SCALE FACTOR? 30 X SHIFT? 120 Y SHIFT? 80 ENTER Y TO REPLOT-N ANGLE OF FLOU? 0 CIRCULATION G/2PI? 25 0 π/20 0 0 - 0 . 13 -0/47 - 0 . 0 4Ε-9 4Ε-9 4Ε-9 +0 Program notes (1) The main part of the program is the same as TRANCl except for an array CP(100) to hold pressure coefficients. The subroutine contains the major changes. (2) In subroutine 3000 the pressure coefficients and force coefficients are calculated from the velocities and the force coefficient printed. Lines 3010 to 3020 input the angle of flow and circulation as in TRANCl.

However, fluid very close to the plate must be slowed by contact with the surface of the plate or slower moving layers of fluid below it. Thus a region of slower moving rotational fluid is established next to the plate and grows thicker in the downstream direction. Outside this region, the boundary layer, the original potential flow solution will still apply. It will be seen that changes in velocity of the fluid occurs very rapidly as the layer is crossed. For example, fluid has zero velocity immediately next to the plate and the full stream velocity just outside the boundary layer.