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Compound Vortex
In the free vortex, v = c/r and thus, theoretically, the velocity becomes infinite at the center. The velocities near the axis would be very high and, skin friction losses vary as the square of the velocity, they will cease to be negligible. Also, the assumption that the total head H remains constant will cease to be true. The portion of fluid around the axis tends to rotate as a solid body. Thus, the central portion essentially forms a forced vortex. The free surface profile of such a compound vortex and the pressure variation with radius on any horizontal plane in the vortex is shown in Figure 5.42.
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vortex Figure 5.42 Compound vortex. |
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For the forced vortex, the velocity at radius R is &R, while for the free vortex, from Equation (5.69), the velocity at radius R is c/R. Therefore, the common radius at which these two velocity will be the same is given by:
mR = c/R
R
