Shut-off Head of Centrifugal Pumps and Fans

A simple model is proposed for estimating the contribution of the volute to the shut-off head of a centrifugal pump or fan. The model is based on an assumed linear distribution of tangential velocity in the plane of the cut water which satisfies approximately the continuity condition of zero net flow into the outlet duct. The contribution of the impeller is assumed to be that given by a solid body rotation at the angular velocity of the pump from the bore of the inlet duct to the impeller tip. The simple radial equilibrium equation is then used to calculate the static head rise in both the impeller and volute.

The resultant prediction of shut-off head, which only requires as input the angular velocity and four radii, has been compared to test data on various pump series made available by courtesy of two European manufacturers. In all of the series the impeller diameter has been varied between 100 and 90–80 per cent of its design value and has been tested in the design volute. Over the series the predicted shut-off head coefficient (gH₃₀/U²₂) was between 1 and 6 per cent lower than the measured values, which themselves varied over the range 0.5–0.6. The predicted contribution from the volute varied typically between 20 and 30 per cent of the total head rise over the range of impeller size, emphasizing the significant contribution from the volute and its dependence on the impeller/volute geometry. Since a review of the available literature did not show any previous work of a fully consistent nature on this topic the proposed model as described in detail below is offered as a fairly accurate prediction technique for design purposes.