Mechanics of Fluids

Those particles next to the forward side of a blade have no choice but to
be hustled forward by it, but particles further from that side tend to deviate
backwards from the prescribed path.
As a result of these two effects – the more ready separation along the back
of a blade and the inertia of the fluid particles – the mean direction of the fluid
leaving the impeller is modified as shown in Fig. 13.33. The velocity vector
diagram that the outlet blade angle φ2 leads us to expect is shown in full: the
figure actually obtained is indicated by dotted lines. Conditions may vary
somewhat round the impeller circumference, but the height of the ‘average’
diagram corresponds to the average value of vr2 (i.e. Q/A 2 ) and therefore,
for a given rate of flow, is unchanged. The backward deviation of R2 results
in a backward shift of the vertex, a reduction in the whirl component vw2
and a consequent reduction in the head produced by the pump.
Methods have suggested for estimating the deviation angle (φ2 − β2) –
which may be as high as 15 ◦ in some designs – but these are still semiempirical.
The greater the number of blades in the impeller the more uniform is the
flow direction, and for an infinite number of blades the deviation of R2 and
hence the whirl slip (see Fig. 13.33) would be zero. Frictional losses, however,
become greater as the number of blades is increased, and the number
of blades used – from six to twelve if they are backward-facing – is a compromise
between these two opposing considerations. Forward-facing blades,
having a convex real surface, greatly encourage the tendency of the flow to
Rotodynamic pumps 633
Fig. 13.32
Fig. 13.33