# Topic: How do I calculate the power for two propellers?

posed by
I'm trying to optimize the mixing time on our tanks. These tanks are used for solid/liquid mixing. I'm using the geometry of the tanks/impellers as well as literature values to try and estimate the mixing time of our tanks and calculate different ways to improve them. My question is more literature based. I'm trying to get the power number from Reynolds number/power number correlation charts to get the mass transfer coefficient that I can use when writing a material balance on the tanks. All of the charts I've seen assume that only one impeller is used, but what if I'm using two propellers on the same shaft? Our tanks aren't baffled, and the propellers are mounted at a 45-degree angle.
• Dave Dickey Forum Moderator 351 Posts

#### Re: How do I calculate the power for two propellers?

The easy answer to your question about using two propellers on the same shaft is that you should calculate the power for each propeller separately and then add the results together.  This calculation works unless the propellers are less than one propeller diameter apart on the shaft.  When the propellers are spaced close together, the total power will be less than the sum of the two calculated power values.  Total power with two closely spaced propellers is typically more than one and a half the power for each propeller, depending on the spacing.

You need to be more concerned about some of your other statements.  What do you mean by the propellers are mounted at a 45-degree angle?  Typically off-center, angle-mounted mixers for unbaffled tanks are mounted at about 15 degrees from the vertical and angled 25 to 30 degrees to the right of the radius.  If the mixer is not mounted correctly, you will see strong rotational or tangential motion, which will not suspend settling particles, but act more like a centrifuge to separate the particles from the liquid.  If you see more than a small vortex on the surface, you probably have an incorrectly mounted mixer.  If you do have rotational motion, you need to use power number/Reynolds number correlations for unbaffled tanks.  Power numbers for unbaffled tanks can be much less than for baffled tanks.  Power typically does not have much effect on the mass transfer coefficient, because the particles tend to move at the same velocity as the adjacent liquid and local turbulence does not extend far from the particle surface.  The dissolution rate is more dependent on particle size and solid liquid equilibrium, both of which affect the concentration driving force.

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• Anonymous CP Reader Community Member 205 Posts

#### Re: How do I calculate the power for two propellers?

Reader Response: The mixers are mounted at 15 degree angle. There is no vortex that takes place deep inside the tank, only on the surface. We're not sure on the distance between the propellers, but from the Re/power number correlation charts we've seen, there doesn't seem to be a factor for the height of the shaft. Do you know how we would calculate the power number for each impeller from the charts? Both propellers have the same diameter and pitch. Our approach involved using a Sherwood=ReNp relation for mixing, getting the mass transfer coefficient from that, calculating the diffusion coefficient from literature/vendor information, and writing a mass balance to determine dissolution rate of the particles. We are assuming these calculations are based on some things like assuming the salt we're using is purely one component. But would you know of any way to account for a salt that isn't pure?

• Dave Dickey Forum Moderator 351 Posts

#### Re: How do I calculate the power for two propellers?

Starting with an answer to the easy question, an estimate of mixer power can be obtained using impeller power numbers.  Assuming your description of the mixer mounting is correct and the fluid motion acts like a baffled tank, the impeller power numbers for different pitch marine props are as follows:  1:1 pitch prop – turbulent power number = 0.35, 1.5:1 pitch prop – power number = 0.62, and 2:1 pitch prop – power number = 1.0.  As recommended before, calculate the power required by each propeller and add the two power values together for the total mixer power.  To calculate power from power number, you will need to know the fluid density, the rotational speed in rpm, and the impeller diameter to within less than 0.1 inch.  Conversion factors may be necessary to correctly calculate power from a dimensionless power number.

I am unaware of a combined relationship for “Sherwood=ReNp.”  Such a relationship does not appear to contain sufficient information to accurately predict a mass-transfer film coefficient.  Calculations for a mass-transfer film coefficient would typically begin with a correlation for Sherwood number as a function of particle Reynolds number and Schmidt number.  The velocity in the Reynolds number is typically the particle settling velocity.  The fluid and mass-transfer properties are in the Sherwood number, Reynolds number, and Schmidt number.  A calculation for settling velocity includes particle size, density and fluid properties.  Particle size distribution will give a range of particle settling velocities, which may change as the particles dissolve.  The point where impeller power should appear in a calculation is for off-bottom suspension, often represented by a just-suspended mixer speed, Njs.  The off-bottom suspension is a function of tank geometry and mixer design.  I am unaware of correlations for off-bottom suspension with angle-mounted propeller mixers.

The mixer power calculations should be straight forward.  I am just not sure that a clear path exists from mixer power to particle film coefficient and particle dissolution time.  Dissolution time is typical determined by laboratory experiment, and is often relatively independent  of mixer power as long as all of the particles are suspended in the liquid.