Question

Textbook:
Theoretical Hydrodynamics”, by L. M. Milne-Thomson, Dover Publication.

In Fig. 6-26 a source is located at a distance a from a wall. What is the total pressure force on the wall? Behind the wall (3 > 0) the pressure is po; the stagnation pressure. Source ܠܠܠܠܠܠܠܠܠܠܠܠܠܠܠܠܠܠܠܠܠܠܠ 1 = = ܣ Image source Fig.6-26

Answer 1

Solution If the flow is given by assuming an image source at x=4 when we place the seat source at x = -4 as Shown in fig. The complex potential for the total flow is sous de " Image Source F = -9 [ln (2+4) + Im (2-4) 83Q (Mm (2+a) + m (7-c)] and to the following dz dź 41 which may be simplified since I axriy ž=xriy v² Q2 (alty?) me (ety?) " - 24" (ahy?) +at]

and from the Bernoullies equation we find the pressuse difference across the wall cat P-Po = -1 v?s, and the total fasse les unit length of the wall (out of papes) on the wall (positive to light) is Force 1 X=0 121_o =-gorta y? dy 20² ) (y?+6²) 2 F.-30? 4IT The negative result indicate that the is to the left and the cell is sucked net the fosce source.