7.1 Define swept volume in an internal combustion engine - NSC Mechanical Technology Automotive - Question 7 - 2019 - Paper 1

1. Remove shims between the cylinder block and cylinder head: This lowers the clearance volume, thereby increasing the compression ratio.

2. Fit thinner cylinder head gasket: A thinner gasket reduces the clearance volume and increases the compression ratio.

3. Machine metal from the cylinder head: This decreases the height of the cylinder head, which effectively increases the compression ratio.

To calculate the swept volume of a single cylinder, we use the given formula:

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

Given:

• Bore diameter (D) = 90 mm = 0.09 m
• Stroke length (L) = 100 mm = 0.10 m

Calculating:

$SV = \frac{\pi (0.09^2)}{4} \times 0.10 ≈ 0.00063617 m^3 = 636.17 cm³$.

Using the relationship between compression ratio (CR), swept volume (SV), and clearance volume (CV), we have:

$CR = \frac{SV + CV}{CV}$

Given:

• Compression ratio (CR) = 10.5,
• Swept Volume (SV) ≈ 636.17 cm³.

Rearranging gives:

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

So:

$CV ≈ \frac{636.17}{10.5 - 1} ≈ 66.97 cm³.$

Let’s denote the original clearance volume as $CV$, which we calculated earlier as approximately 66.97 cm³.

With the new compression ratio:

$11 = \frac{SV + CV}{CV}$

We need to find the new swept volume $SV$:

$SV = CV \times (CR - 1)$ $SV = 66.97 \times (11 - 1) = 669.7 cm³.$

We can now use this value to find the new bore diameter.

Using the formula for swept volume:

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

• $L$ = 100 mm = 0.1 m
• Rearranging gives: $D^2 = \frac{4 \times SV}{\pi L}$ After substituting in:

$D^2 = \frac{4 \times 669.7 \times 10^{-6}}{\pi \times 0.1}$

After calculation, we find: $D \approx 9.23 cm = 92.34 mm.$

Indicated Power (IP) can be calculated using the formula:

$IP = P \times L \times A \times N \times n$

Where:

• Mean effective pressure ($P$) = 1300 kPa = 1300000 Pa,
• Stroke length ($L$) = 160 mm = 0.16 m,
• Area of the bore ($A$) is given by: $A = \frac{\pi D^2}{4} = \frac{\pi (0.12^2)}{4} = 0.0113 m^2,$
• Engine speed ($N$) = 4500 r/min = 75 r/s,
• Number of cylinders ($n$) = 4.

Putting all values into the formula gives:

$IP ≈ (1300000) \times (0.16) \times (0.0113) \times (75) \times (4) ≈ 352.56 kW.$

The Brake Power (BP) can be calculated using:

$BP = 2 \pi \times N \times T / 60$

Where:

• Torque ($T$) = 610 Nm,
• Engine speed ($N$) = 4500 r/min.

Thus:

$BP = 2 \times \pi \times 610 \times (4500/60) ≈ 28745.73 W = 28.75 kW.$

The mechanical efficiency ($\eta$) of the engine can be calculated as:

$\eta = \frac{BP}{IP} \times 100$

Where:

• Brake Power (BP) = 28745.73 W,
• Indicated Power (IP) = 352.56 kW = 352560 W.

Thus: $\eta ≈ \frac{28745.73}{352560} \times 100 ≈ 81.54\%.$

Mechanical efficiency is defined as the ratio of the brake power (the power available at the engine shaft) to the indicated power (the total power generated by the combustion process inside the engine). It is a measure of how effectively the engine converts the fuel's energy into useful work.

Mathematically, it can be expressed as:

$\eta = \frac{BP}{IP} \times 100.$

Brake power (BP) is the actual power output of an internal combustion engine at the crankshaft, measured in mechanical work. This value represents the engine's effective output capabilities after losses due to friction, heat, and other factors have been accounted for. It is an important measurement for assessing an engine's performance and efficiency.