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Radial Thrust Due to Total Dynamic Head
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The radial force is due to the uneven pressure distribution in the pump casing. It is expressed as: 
                                           
                                                     FR=K*ᵨgHd2*B2
where
d2 = tip diameter of the impeller vanes
B2 = width of the pump casing

                                                  B2 = b2 + xf + xb

Wear can chip at the surface of the impeller or the casing, thus causing an increase of xf and xb and a reduction of b2 through the life of the pump.

The value of K may be as high as 0.40 near the shut-off head and as low as 0.10 at the best efficiency point. It is, however, recommended to conduct proper measurements with proximity probes over the envelope of the flow rate during the design of a new pump. The proximity probes are used to measure the deflection at the gland. The magnitude of the force is then calculated from cantilever stress theory.
 
As shown in Figure 8-30, different shapes of volutes give different values for the radial load. Stepanoff (1993) clearly indicated that the direction of the radial force reverses after the best efficiency point, whereas Angle et al. (1997) do not seem to agree with this supposition. A misunderstanding of the direction of this hydraulic radial force leads to totally different estimation of the bearing life. A calculation that assumes a zero radial load
near the best efficiency point (following the Stepanoff approach) can lead to a bearing life ten times as high as another calculation that assumes that the same radial load adds to the weight of the impeller, creating a large bending moment on the shaft and reaction loads at the bearings. A smart salesman may try to convince the consultant slurry engineer of the superiority of his product over the competition in terms of the rigidity of the bearing assembly, whereas in reality it is a matter of adding or subtracting loads.
 
Shafts of slurry pumps have broken at the shaft thread, simply because the radial load was too high and caused rapid fatigue failure. It is therefore strongly recommended to limit the minimum flow rate to half the best efficiency flow rate at the given speed. Throttlingan oversize pump is not recommended at all. Downsizing or reducing the speed of the pump is essential to avoid excessive radial load on the pump shaft.
 
Each manufacturer has their recommended value of K for the calculation of the radial load and the bearing life.

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