The size of a flywheel for a multi-cylinder engine is smaller compared to a single-cylinder engine. This is because a multi-cylinder engine inherently provides better balance and smoother operation, reducing the need for a large flywheel.

1. Importance of a Flywheel:
A flywheel is a rotating mechanical device that stores and releases kinetic energy to smooth out the fluctuations in the speed of an engine. It helps maintain a constant speed during the power stroke and stores energy during the power stroke to deliver it back during the rest of the cycle.

2. Work per Cycle:
The work per cycle is the amount of work done by the engine during one complete cycle. For the same indicated work per cycle, both single-cylinder and multi-cylinder engines will produce the same amount of work.

3. Mean Speed:
Mean speed refers to the average speed of the engine during one complete cycle. In a single-cylinder engine, the mean speed is equal to the speed of the engine. However, in a multi-cylinder engine, due to the firing order and arrangement of cylinders, the mean speed is higher than the speed of the engine.

4. Permissible Fluctuation of Speed:
Fluctuations in the speed of an engine occur due to variations in the power produced during each cycle. The permissible fluctuation of speed is the acceptable range within which the speed can vary without affecting the overall performance of the engine. In general, a smaller fluctuation of speed is desirable for smooth operation.

5. Comparison of Single-Cylinder and Multi-Cylinder Engines:
In a single-cylinder engine, the power produced during each cycle is uneven, causing significant fluctuations in speed. To compensate for this, a larger flywheel is required to store and release more energy, reducing the effect of speed variations.

On the other hand, a multi-cylinder engine produces a more balanced and smoother power delivery due to the firing order and arrangement of cylinders. This results in smaller fluctuations in speed compared to a single-cylinder engine. As a result, a smaller flywheel is sufficient to smooth out the speed fluctuations in a multi-cylinder engine.

Therefore, for the same indicated work per cycle, mean speed, and permissible fluctuation of speed, a multi-cylinder engine requires a smaller flywheel compared to a single-cylinder engine.