Question

The area under the turning moment diagram represents

• A. Mean turning moment
• B. Maximum torque to which the crankshaft is subjected to
• C. Power developed by the engine
• D. Work done per cycle

Hint:

The area under the turning moment diagram gives the work done per cycle, with units \( \text{Nm} \cdot \text{radians} = \text{Joules} \).

Answer 1

The Correct Option is D

Step 1: Understand the turning moment diagram.
The turning moment diagram (also called a torque diagram) plots the torque (or turning moment) acting on the crankshaft of an engine versus the crank angle (or time) over one cycle. The area under this diagram represents a physical quantity related to the engine’s performance. Step 2: Analyze the area under the diagram.
The turning moment \( T \) (in Nm) is plotted against the crank angle \( \theta \) (in radians).
The area under the curve \( \int T \, d\theta \) has units of \( \text{Nm} \cdot \text{radians} \), which is the unit of work (or energy), since \( \text{Nm} = \text{Joules} \), and radians are dimensionless.
For one complete cycle (e.g., \( 0 \) to \( 2\pi \) for a four-stroke engine), the area under the turning moment diagram is:
\[ \text{Area} = \int_0^{2\pi} T \, d\theta, \] which represents the work done per cycle by the engine. Step 3: Evaluate the options.
(1) Mean turning moment: The mean turning moment is the average torque, calculated as the area under the diagram divided by the angle (e.g., \( \frac{\text{Area}}{2\pi} \)), not the area itself. Incorrect.
(2) Maximum torque to which the crankshaft is subjected to: The maximum torque is the peak value on the diagram, not the area under it. Incorrect.
(3) Power developed by the engine: Power is work per unit time, i.e., \( \text{Power} = \frac{\text{Work}}{\text{Time}} \). The area gives work, not power directly. Incorrect.
(4) Work done per cycle: As derived, the area under the turning moment diagram directly represents the work done per cycle. Correct.
Step 4: Select the correct answer.
The area under the turning moment diagram represents the work done per cycle, matching option (4).