Trommel critical speed in rpm: give the formula in terms of trommel diameter D (ft).

Introduction / Context:
Critical speed indicates the rpm at which particles would centrifuge against the shell rather than tumble. For screening action, operation is kept well below this limit. Engineers use a convenient rpm–diameter relation for quick estimates.

Given Data / Assumptions:

• D = trommel diameter in feet.
• Standard gravity and unit conversions embedded in the constant.
• Ignoring liner thickness and particle lift.

Concept / Approach:
Starting from N (rps) = (1/(2π)) * √(g/r) with r = D/2, converting to rpm and feet leads to N_rpm ≈ 76.75 / √D. This is analogous to the mill critical-speed formula used in comminution texts.

Step-by-Step Solution:
Use r = D/2 and convert to rpm: N_rpm = 60/(2π) * √(g/r).Insert g and unit conversions (ft): yields ≈ 76.75 / √D.Select the option matching this relation.

Verification / Alternative check:
Handbooks quote 76.6–76.8 as the constant depending on rounding; any of these near 76.7 is acceptable in practice.

Why Other Options Are Wrong:
Multiplying by D or √D or dividing by D does not follow from the critical-speed derivation, which scales with 1/√D.

Common Pitfalls:
Using diameter in metres while keeping the imperial constant, or forgetting to subtract media diameter in grinding-mill cases.

Final Answer:
76.75 / √D