A four cylinder four stroke spark ignition engine has a bore of 80 mm and stroke of 80mm. The compression ratio is 8. Calculate;(i) The engine capacity. (3 marks)(ii) The clearance volume of each cylinder
Question
A four cylinder four stroke spark ignition engine has a bore of 80 mm and stroke of 80mm. The compression ratio is 8. Calculate;(i) The engine capacity. (3 marks)(ii) The clearance volume of each cylinder
Solution 1
(i) The engine capacity (also known as displacement) can be calculated using the formula:
V = π/4 * B² * S * N
where: V is the engine capacity, B is the bore diameter, S is the stroke length, and N is the number of cylinders.
Substituting the given values:
V = π/4 * (80mm)² * 80mm * 4
V = π/4 * 6400mm² * 80mm * 4
V = 1,605,776 mm³
Since 1 cubic centimeter (cc) is equal to 1,000 cubic millimeters, the engine capacity is 1,605.776 cc or approximately 1.6 liters.
(ii) The clearance volume (Vc) can be calculated using the formula derived from the compression ratio (CR):
CR = (V + Vc) / Vc
where: CR is the compression ratio, V is the displacement volume, and Vc is the clearance volume.
Rearranging the formula to solve for Vc gives:
Vc = V / (CR - 1)
Substituting the given values:
Vc = 1,605,776 mm³ / (8 - 1)
Vc = 229,396 mm³
Again, converting to cubic centimeters gives a clearance volume of approximately 229.4 cc.
Solution 2
(i) The engine capacity (also known as displacement) can be calculated using the formula:
V = π/4 * B² * S * N
where: V is the engine capacity, B is the bore diameter, S is the stroke length, and N is the number of cylinders.
Substituting the given values:
V = π/4 * (80mm)² * 80mm * 4 V = π/4 * 6400mm² * 80mm * 4 V = 1,605,776 mm³ or 1.61 liters (since 1 liter = 1,000,000 mm³)
(ii) The clearance volume (Vc) can be calculated using the formula derived from the compression ratio (CR):
CR = (V + Vc) / Vc
where: CR is the compression ratio, V is the displacement volume, and Vc is the clearance volume.
Rearranging the formula to solve for Vc gives:
Vc = V / (CR - 1)
Substituting the given values:
Vc = 1,605,776 mm³ / (8 - 1) Vc = 229,396 mm³ or 0.23 liters per cylinder.
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