Subtopic: Thermodynamic principles of I.C. engines
Question Statement:
In a 4-stroke single cylinder diesel engine, the inlet valve opens at 10⁰ before TDC and closes at 40⁰ after BDC. The exhaust valve opens at 25⁰ before BDC and closes at 15⁰ after TDC. The percentage of time for which both the valves remain closed in one cycle of the engine is
Options:
(A) 32.29
(B) 40.97
(C) 46.53
(D) 75.01
Official Answer Key:
B
Step-by-Step Solution & Explanation
One full 4-stroke cycle spans 720° of crank rotation. Measuring crank angle θ continuously from intake TDC (θ=0):
Intake valve open window: from −10° (=710°) to 180+40=220° → total open duration = 10+220 = 230°, spanning [710°,720°]∪[0°,220°].
Exhaust valve open window: opens 25° before BDC (θ=540°), i.e. at 515°; closes 15° after TDC (θ=720°/0°), i.e. at 15° → total open duration = 205+15 = 220°, spanning [515°,720°]∪[0°,15°].
Union of the two open windows: [0°,220°] ∪ [515°,720°] (since [710,720] and [0,15] fall inside these), total = 220+205 = 425°.
Both-closed duration = 720−425 = 295°. Percentage = 295/720×100 = 40.97%. Answer: (B).
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