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When an impeller operates in turbulent flow, the loads on each blade are fluctuating about a mean. To better visualize this, imagine riding along in a car with your hand outside the window. You will note that your hand is buffeted about, with a highly variable force. This is due to turbulence, involving various shedding of vortices, etc. The same thing happens to an impeller in turbulent flow. The load on each blade varies with time, and the loads on each blade are not synchronous with each other. The result is that there will be a fluctuating net side load on the impeller, creating a bending load on the shaft. This load, sometimes called an imbalanced hydraulic force, is not due to mechanical imbalance or any lack of manufacturing precision. It is entirely due to the nature of turbulence.

The dimensionless hydraulic force equals the product of hydraulic force times impeller diameter divided by impeller torque:

(3.12)

Normally, the peak value of this ratio is correlated, so that a peak value of hydraulic force may be predicted and used in shaft and impeller design. This group is a function of Reynolds number and impeller type, as well as geometric ratios, aeration number, and Froude number, and direction of pumping for axial flow impellers.