Question

The torque (in N-m) exerted on the crank shaft of a two stroke engine can be described as T = 10000 + 1000 sin 2θ – 1200 cos 2θ, where θ is the crank angle as measured from inner dead center position. Assuming the resisting torque to be constant, the power (in kW) developed by the engine at 100 rpm is __________.

Answer 1

The power developed by the engine at 100 rpm is calculated using the average torque and the angular velocity. Since the average torque is the constant term of the torque equation provided, it is 10000 N.m. The power is found by multiplying this torque by the angular velocity converted from rpm to rad/s.

Step-by-step explanation:

To calculate the power developed by a two-stroke engine at a given rpm, we use the equation provided for the torque exerted on the crankshaft, T = 10000 + 1000 sin 2θ – 1200 cos 2θ, where θ is the crank angle. At a rotary speed of 100 revolutions per minute (rpm), we convert this to radians per second (ω) by using the relation ω = rpm × (2π/60). To determine the power output in kilowatts (kW), we use the formula P = Tω where T is the average torque over one full cycle.

As we are given a periodic torque function, the average value of the sinusoidal part over a full cycle is zero. Therefore, the average torque is just the constant term, which is 10000 N.m. At 100 rpm, the angular velocity ω = 100 × (2π/60) rad/s. The power developed by the engine can then be calculated as P = 10000 N.m × ω and converted into kW by dividing by 1000.