There are some complex formulas (differential equations) for calculating the actual force of a moving fluid against an obstruction. However, a simple but rough estimate that is commonly used for water is

Force (lbs) = Area (ft2) x K x Velocity2 (ft/sec) where K is a drag coefficient. For a rectangular flat obstruction, K can be between 1.8 and 2.0.

So using K = 2, a rectangular paddle of area 10 ft2 against a water velocity of 6 ft/sec (4.1 mph) would produce

10 x 2 x 62 = 720 lbs force

Of course it will be necessary to compute the velocity of the paddle based on the rotating speed and radius of the wheel. The torque will simply be the calculated force x the radius of the center of the paddle.

There are at least two other complicating factors that need to be considered: • More than one paddle may be active at any instant, increasing force; • The relative velocity of the water will change from startup to running condition as the momentum of the water in the channel increases, decreasing force.

One could ass-u-me that these two may cancel, or some reasonable factor guess-timates could be made to tune the results, or at least determine a range of possible result values.

Hydraulic engineering firms would use CFD (Computational Fluid Dynamics) software to model the problem.


Editor's Note: This question was answered by Gene Vogel, Electrical Apparatus Service Association. Our Motors & Drives experts, Tom Bishop and Chuck Yung, technical support specialists at EASA, asked Gene to field this question.