# A 2 ft diameter trommel screen is used to separate municipal refuse.

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A 2 ft diameter trommel screen is used to separate municipal refuse. Estimate its critical speed.

asked Mar 4, 2014 in Others

## 1 Answer

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The critical speed ($N_c$ of a trommel screen is the speed necessary to hold the materials contained against the wall throughout a complete revolution and is given in rotations per sec. The only forces acting on particles along the wall are the normal force and gravity which should cause circular motion. The minimum rotational velocity of the trommel will result in no normal force at the top of the rotation of the trommel.

$$F = m r \omega^2= mg$$

$$\omega = 2 \pi N_c$$

So our critical speed is:

$$N_c = \sqrt{ \frac{ g}{4 \pi^2 r}}$$

Keep in mind that g and r need to be in similar units (feet per sec^2 and feet).
answered Mar 10, 2014 by (2,140 points)