How do you calculate torque requirements for a paddle wheel used to move water in a pond? I need to know torque in order to size a motor and gear reducer for a paddle wheel.
Topic: How do you calculate torque requirements for a paddle wheel used to move water in a pond?
21 June 2010
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Re: How do you calculate torque requirements for a paddle wheel used to move water in a pond?
21 June 2010 at 1:29pmThere 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 (ft^{2}) x K x Velocity^{2} (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 ft^{2} 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 assume that these two may cancel, or some reasonable factor guesstimates 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.

Re: How do you calculate torque requirements for a paddle wheel used to move water in a pond?
7 November 2014 at 12:39pmThere are a number of ways to calculate this torque but all theories need to be validated in the field. I have a patented design on a completely submerged water wheel and I have setup a torque testing platform. Sorry if this is a little late, I noticed that this was posted in 2010. If you're interested I send you pictures of the torque platform. It's very difficult to get flow rates of greater than 4 ft/s in local areas. Let me know if I can help. Thx Paul
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