7.1 Define swept volume of an engine - NSC Mechanical Technology Automotive - Question 7 - 2022 - Paper 1

To calculate the swept volume (SV), we can use the formula:

SV = rac{ ext{π} imes D^2}{4} imes L

Where:

• D is the bore (diameter) in cm
• L is the stroke length in cm.

For this question:

• D = 12 cm (120 mm converted to cm)
• L = 13.5 cm (135 mm converted to cm)

Plugging in the values:

SV = rac{ ext{π} imes (12)^2}{4} imes 13.5 = rac{3.1416 imes 144}{4} imes 13.5 \ = 1,526.81 ext{ cm}^3

The compression ratio (CR) is calculated using the following formula:

CR = rac{SV + CV}{CV}

Where:

• SV is the swept volume calculated earlier as 1,526.81 cm³
• CV is the clearance volume, given as 102.5 cm³.

Substituting the values:

CR = rac{1,526.81 + 102.5}{102.5} = rac{1,629.31}{102.5} \ = 15.9:1

The indicated power can be calculated using the following relation:

P = rac{(P_{m} imes L imes A imes N)}{60} imes n

Where:

• P_{m} is the mean effective pressure (1,150 kPa, convert to Pa)
• L is stroke length in meters (0.077 m for 77 mm)
• A is the cross-sectional area of the cylinder:

A = rac{ ext{π} imes D^2}{4} = rac{3.1416 imes (0.1)^2}{4} = 7.85 imes 10^{-3} m^2

• N is number of revolutions per minute (1,800 r/min)
• n is number of cylinders (4)

Substituting values and calculating the power:

P = rac{(1,150,000 imes 0.077 imes 7.85 imes 10^{-3} imes 1,800)}{60} imes 4 = 157.08 kW

The torque ( au) can be calculated using the formula:

$$au = ext{Force} imes ext{radius}$$

Where the force is the weight:

$$ext{Force} = m imes g = 120 imes 10 = 1200 N$$

And the radius in meters is:

ext{radius} = rac{500}{1000} = 0.5 m

Thus,

$$au = 1200 imes 0.5 = 600 Nm$$

The brake power can be calculated using the formula:

$$P_{B} = 2 imes ext{π} imes n imes au$$

Substituting the values:

• n = 2500 r/min (RPM here indicates revolution per minute)
• au = 600 Nm

Thus,

P_{B} = 2 imes 3.1416 imes rac{2500}{60} imes 600= 157.08 kW

Mechanical efficiency ( ext{ME}) can be calculated by the formula:

ext{ME} = rac{B.P}{I.P} imes 100

Substituting the values:

• Brake power (B.P) = 157.08 kW
• Indicated power (I.P) = 196 kW

Thus,

ext{ME} = rac{157.08}{196} imes 100 \ ext{ME} ext{ approximately equals } 80.14 \%