Correct Answer - Option 2 : 39.4
Concept:
Uniform Pressure Theory
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Uniform Wear Theory
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p = constant
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p × ri = constant
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\({T_f} = \frac{{2\pi μ p}}{3}\left( {r_o^3 - r_i^3} \right)\)
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\({T_f} = \pi μ p{r_i}\left( {r_o^2 - r_i^2} \right)\)
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Power = ω × Tf
Calculation:
Given:
Power (P) = 5 kW ⇒ 5 × 103 W, N = 2000 rpm, μ = 0.25, ri = 25 mm and p = 1 MPa ⇒ 1 N/mm2
Power = ω × Tf
\(P = \frac{2\pi{N}}{60}× T_f\)
⇒ \(5 × 10^{3}=\frac{2\pi\;×\;{2000}}{60}× T_f\)
∴ Tf = 23.873 × 103 N-mm.
For Uniform Pressure Theory, the Torque carrying capacity is given by -
\({T_f} = \frac{{2\pi μ p}}{3}\left( {r_o^3 - r_i^3} \right)\)
⇒ \(23.873\;\times\;10^{3}=\frac{2\pi\;\times\;0.25\;\times\;1}{3}(r_o^{3}\;-\;25^3)\)
∴ ro = 39.41 mm.