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Finding the Hydraulic Load

Q: How do I find the hydraulic load to calculate the shaft deflection of a vessel agitator? A mixing agitator incorporates a six-blade turbine impeller (90 degree - flat) that spins at 650 rpm to mix 200L of a water-like fluid in a 260L fermenter. The tank has a 31" ID. What is the calculation used to determine the hydraulic load at this high rate of mixing? The impeller pulls a vortex to the bottom of the vessel, so it is not fully submerged in the fluid at all times. The next step would be to then calculate the shaft deflection that is experienced with this hydraulic load.

A: With the additional information and drawings provided, the lateral hydraulic force at the impeller is estimated to be 11 lbs.  That load is 3.0 times the load estimated for a fully submerged impeller.  The 1-hp motor is loaded to about 3/4 horsepower, without baffles in the tank.  The lack of baffles in the tank reduces the power input for the described conditions, but also greatly reduces the effectiveness of the agitator for both bulk mixing and gas dispersion.  The shaft deflection is estimated to be 0.042 inches.  With assumptions of a bearing in the seal housing and an estimated impeller weight of 13 lbs, the shaft natural frequency will be near 730 rpm, which could cause severe vibration with the mixer operating at 650 rpm.  Without details of the bearing supports and impeller weight, the critical speed is only an estimate.
 
For a data sheet the will provide more information about the mixer design and performance, click here.

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