# Topic: Do I need to calculate the Froude number for a paddle blender?

posed by  Last edited: 10 June 2013 At 9:41am
I want to calculate the motor horsepower for a paddle blender for mixing liquid chocolate, which has a viscosity of 18,000 cp. I have calculated using Reynolds number and Power number but was not sure enough. Someone told me to calculate Froude's number. Is it really necessary?
• Dave Dickey Forum Moderator 324 Posts

#### Re: Do I need to calculate the Froude number for a paddle blender?

To calculate motor HP for a paddle blender mixing liquid chocolate at 18,000 cp, the Reynolds number is needed to determine the appropriate power number at the operating conditions.  The power number for turbulent conditions must be corrected for the effect of viscosity associated with the Reynolds number at 18,000 cp.  Froude number is only relevant for a low viscosity fluid in an unbaffled tank with strong rotational flow and a deep surface vortex.  Froude number represents the ratio of inertial to gravitational forces.  Most applications on earth operate at the same gravity, so even with a low viscosity fluid and proper baffles the effect of Froude on power is negligible.

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• Abhinay Kumar Community Member 1 Post

#### Re: Do I need to calculate the Froude number for a paddle blender?

In practical the flow is turbulent for which the Reynolds number must be greater than 2100 but as per my calculation the Reynolds number came around 39 which represents the laminar flow. So kindly advice how to proceed for the calculation and what are the methods or conditions i should consider which provide me the adequate result.
• Dave Dickey Forum Moderator 324 Posts

#### Re: Do I need to calculate the Froude number for a paddle blender?

Before we proceed, we need to start over.  Your question asks a good question, but you evidently did not calculate a mixing Reynolds number.  A value of 2,100 is not a turbulent Reynolds number for a mixer.  A mixing Reynolds number is impeller diameter squared times rotational speed times density divided by viscosity (Re = D^2 N rho / mu).  The Reynolds number is dimensionless, so you need to be sure that the units cancel out.  For a mixing Reynolds number, turbulent conditions exist above 20,000 and laminar conditions exist below 10.  Between 20,000 and 10, you have transitional motion.  The impeller power number is impeller power divided by the quantity (density times rotational speed cubed times impeller diameter to the fifth power [Np = P / (rho N^3 D^5)].  The power number is also dimensionless.  The impeller power number usually is constant for turbulent conditions and inversely proportional to Reynolds number fr viscous conditions.  Power number changes gradually (typically increasing) in the transition range.  An impeller power number is an empirical quantity developed from measurements of geometrically similar devices.  You still do not need to know how to calculate the Froude number, although there is a definition for mixers.

The equipment term "paddle blender" is very generic, so you have not provided sufficient specific information to do calculations. You said you had a power number, which is usually a turbulent power number obtained from a reference or equipment supplier.  The value you have for your power number will depend on the type of paddle you have.  Power number is not a generic quantity.  Depending on the Reynolds number you have for your mixer operating with an 18,000 cp fluid, you need to make a correction to the turbulent power number.  You then need to rearrange the power number to calculate the power.  Power equals power number (a function of Reynolds number) times density times rotational speed cubed times impeller diameter to the fifth power (P = Np' rho N^3 D^5), in the appropriate units.

If this explanation does not make sense to you, you will need to supply more information about your equipment.  You also need to be sure that your viscosity is actually 18,000 cp.