7.1 Define the following terms: 7.1.1 Power 7.1.2 Compression ratio 7.2 The bore of an engine is 70 mm and the stroke is 75 mm - NSC Mechanical Technology Automotive - Question 7 - 2021 - Paper 1

The compression ratio is the ratio of the total volume of the cylinder when the piston is at bottom dead center (BDC) to the volume in the cylinder when the piston is at top dead center (TDC). It is given by:

$CR = \frac{V_{total}}{V_{cylinder}}$

The swept volume (SV) can be calculated using the formula:

$SV = \frac{\pi D^2}{4} \times L$

where:

• $D = 70$ mm
• $L = 75$ mm

Converting to cm: $SV = \frac{\pi (7)^2}{4} \times 7.5 \approx 288.63 \text{ cm}^3$

The original clearance volume (CV) can be determined from the compression ratio:

$CV = \frac{SV}{CR - 1}$

where:

• $CR = 9.5$
• $SV \approx 288.63$ cm³

Thus, $CV = \frac{288.63}{9.5 - 1} \approx 33.96 \text{ cm}^3$

The new compression ratio is 10:1, and the clearance volume remains unchanged. Rearranging the formula for the new diameter:

$CR = \frac{SV + CV}{CV}$ Substituting values: $10 = \frac{SV + 33.96}{33.96}$ This gives: $SV = 33.96 \times (10 - 1) \approx 305.64 \text{ cm}^3$ Rearranging for diameter: $D = \sqrt{\frac{SV \times 4}{\pi \times L}}$ Substituting: $D = \sqrt{\frac{305.64 \times 4}{\pi \times 7.5}} \approx 72.03 ext{ mm}$

Torque can be calculated from the force and the radius:

$Torque = Force \times Radius$ Here:

• Force from the spring balance reading is 25 kg, which equals: $Force = 25 \times 9.81 = 245.25 ext{ N}$
• Radius is 420 mm or 0.42 m: $Torque = 245.25 \times 0.42 = 103.15 ext{ N.m}$.

Indicated Power (IP) can be calculated as:

$IP = \frac{MAP \times A \times N \times 60}{1000}$

• MAP = 900 kPa = 900,000 Pa
• Area $A$ of the cylinder: $A = \frac{\pi D^2}{4} \Rightarrow A = \frac{\pi (0.084)^2}{4} \approx 0.00554 \text{ m}^2$
• N (number of power strokes) per minute: $N = \frac{2000}{2} = 1000 ext{ power strokes/min}$ Finally, substituting: $IP = \frac{900000 \times 0.00554 \times 1000}{1000} \approx 28.60 ext{ kW}$

Brake Power (BP) can be calculated using the formula:

$BP = 2 \pi NT$

Substituting values:

• N = 2000/60 = 33.33 power strokes/sec
• T = 105 N.m Thus, $BP = 2 \times \pi \times 33.33 \times 105 \approx 22.05 ext{ kW}$

Mechanical efficiency can be calculated as:

$\text{Mechanical Efficiency} = \frac{BP}{IP} \times 100$ Thus, $\text{Mechanical Efficiency} = \frac{22.05}{28.60} \times 100 \approx 77.05 \%$