Here is the question, explain why 9/10 was used to multiply 500: Find out the speed at which a four-cylinder engine using natural gas can develop a brake power of 50kW working under following conditions. Air-gas ratio 9:1, calorific value of the fuel = 34 MJ/m³, compression ratio 10:1, volumetric efficiency = 70%, indicated thermal efficiency = 35% and the mechanical efficiency = 80% and the total volume of the engine is 2 litres.

The compression ratio ($CR$) is given as $10:1$. The compression ratio is defined as:

$$CR = \frac{\text{Total Volume}}{\text{Clearance Volume}} = \frac{V_s + V_c}{V_c}$$

From this definition, we can also express the swept volume ($V_s$) in terms of the total volume ($V_{tot}$) and the compression ratio ($CR$).

We know that $V_{tot} = V_s + V_c$.
From the compression ratio definition:

$$CR = \frac{V_{tot}}{V_c} \implies V_c = \frac{V_{tot}}{CR}$$

Now substitute $V_c$ back into the equation for $V_{tot}$:

$$V_{tot} = V_s + \frac{V_{tot}}{CR}$$

Rearrange to solve for $V_s$:

$$V_s = V_{tot} - \frac{V_{tot}}{CR}$$ $$V_s = V_{tot} \left(1 - \frac{1}{CR}\right)$$ $$V_s = V_{tot} \left(\frac{CR - 1}{CR}\right)$$

Given:

• $V_{tot}$ per cylinder = $500 \text{ cc}$ (from the previous step, $2 \text{ litres} / 4 \text{ cylinders} = 0.5 \text{ litres} = 500 \text{ cc}$)
• $CR = 10$

Substitute these values into the formula for $V_s$:

$$V_s = 500 \text{ cc} \times \left(\frac{10 - 1}{10}\right)$$ $$V_s = 500 \text{ cc} \times \left(\frac{9}{10}\right)$$

Therefore, $\frac{9}{10}$ is used to multiply $500 \text{ cc}$ to calculate the swept volume ($V_s$) per cylinder, which is the volume displaced by the piston as it moves from Bottom Dead Center (BDC) to Top Dead Center (TDC).