Difficulty: Medium
Correct Answer: HP = (2 * π * N * T) / 4500
Explanation:
Introduction / Context:
Converting rotational speed and torque to power is essential for machine and drivetrain design. When torque is in kg·m and power is desired in horsepower, consistent unit conversion must be applied.
Given Data / Assumptions:
Concept / Approach:
Mechanical power P (in kgf·m/s) equals torque times angular speed: P = T * ω. With ω = 2πN/60, and converting to HP using 1 HP = 75 kgf·m/s, we obtain the standard Indian practice formula.
Step-by-Step Solution:
1) Angular speed ω = 2πN / 60 rad/s.2) Power in kgf·m/s: P = T * ω = T * (2πN/60).3) Convert to HP: HP = P / 75 = [T * (2πN/60)] / 75.4) Simplify: HP = (2π N T) / (60 * 75) = (2π N T) / 4500.
Verification / Alternative check:
Using SI units: if T were in N·m and N in rpm, power in watts would be P = 2πN T / 60. Converting N·m to kgf·m and watts to HP yields the same final constant 1/4500 for kgf·m inputs.
Why Other Options Are Wrong:
Expressions missing the 4500 denominator ignore the dual conversion from rpm to per second and from kgf·m/s to HP.Variants with 2250 or 75 stem from algebraic or unit slips.
Common Pitfalls:
Mixing torque units (N·m vs kgf·m) and misusing the HP conversion factor; forgetting that N is per minute, not per second.
Final Answer:
HP = (2 * π * N * T) / 4500
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