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Question

Derive an expression for the maximum torque needed to rotate an agitator if it depends on the frequency of oscillation, the angular velocity with which the agitator rotates during an oscillation, the diameter of the agitator, the nominal height of the paddles, the length of the paddles, the number of paddles, the depth of liquid, and the liquid density.

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In this exercise, we are asked derive an equation for the maximum torque $T$ required to rotate an agitator. The given variable parameters are listed below:

- $T$ - torque
- $f$ - frequency of oscillation
- $\omega$ - angular velocity
- $D$ - diameter of agitator
- $h$ - height of paddles
- $l$ - length of paddles
- $n$ - number of paddles
- $d$ - depth of liquid
- $\rho$ - liquid density

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