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In a brake test, the DC motor took 20 A from a 200 V supply mains. The brake pulley of radius 10 cm had an effective load of 20 kg and the speed was 10 rps. The value of BHP (in metric) is ______.
1.3π
0.2π
0.5π
8.8π
0.5π
The Brake Horsepower (BHP) is calculated by determining the mechanical power developed at the shaft. Given the torque τ and angular velocity ω, the power is P=τ×ω, converted to metric horsepower.
The Brake Horsepower (BHP) is calculated by determining the mechanical power developed at the shaft. Given the torque τ and angular velocity ω, the power is P=τ×ω, converted to metric horsepower.
τ=m×g×r⟹20×9.81×0.1=19.62 Nm
BHP=735.52πNτ
Metric HP=735.52π×10×19.62≈1.67 HP
In a brake test (Prony brake), the load W (in kg) acts at a radius r (in meters) to create a torque τ=W×9.81×r Newton-meters. The mechanical power is then calculated as P=2πNτ Watts, where N is speed in revolutions per second. The result is converted to metric BHP by dividing by 735.5 W.
The input electrical power (20 A at 200 V) is used to find efficiency, but BHP depends only on mechanical output.
The term 'Metric HP' in India is defined as 735.5 Watts.
Calculation: Power (Watts)=2π×10×19.62≈1232.5 W.
BHP=735.51232.5≈1.67. Note: If we use g=10 m/s2 and 1 HP=750 W (approximation), the result simplifies to 0.5π.
Direct measurement of mechanical power output
Simple test setup for small DC machines
Low efficiency as power is dissipated as heat
Limited to small capacity motors due to friction constraints
Efficiency testing of small DC motors
Laboratory characterization of rotating machines
If we take g=9.81 m/s2, the answer is roughly 1.67. Using g=10 and 1 Metric HP=735.5 W, the calculation is 735.5×1002π×10×20×10≈0.54π. The provided answer 0.5π assumes common textbook simplifications.
Option A is significantly higher; Option B and D are distractors based on incorrect radius or speed units.
C is correct — The BHP calculation using the standard load-torque relationship yields approximately 0.5π under typical academic simplification.
Always verify if the exam board uses g=9.81 or g=10 and 1 HP=735.5 W or 746 W before starting the calculation.
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