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Four cylinder, four stroke S.I. engine develops maximum braking torque of 200 N-m at 2500 rpm. At maximum engine torque, brake mean effective pressure is 750 kPa. Diameter of bore is equal to length of stroke. Engine capacity is:-

  • a) 
    833 cc
  • b) 
    900 cc
  • c) 
    3600 cc
  • d) 
    3332 cc
Correct answer is option 'D'. Can you explain this answer?
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Given data:
Maximum Braking Torque (T) = 200 N-m
Engine Speed (N) = 2500 rpm
Brake Mean Effective Pressure (BMEP) = 750 kPa
Diameter of Bore (D) = Length of Stroke (L)

To find: Engine Capacity

Formula used:
Brake Mean Effective Pressure (BMEP) = (Pmax + Pmin)/2
Where,
Pmax = Maximum pressure in cylinder
Pmin = Minimum pressure in cylinder

Brake Power (BP) = 2πNT/60

Mean Effective Pressure (MEP) = BP/Vd
Where,
Vd = Displacement volume

Torque (T) = BP/2πN

Calculation:
BMEP = (Pmax + Pmin)/2
Pmax = BMEP + Pmin
At maximum torque, Pmin = 0
Pmax = BMEP = 750 kPa

Torque (T) = BP/2πN
BP = 2πNT/60
T = BP/2πN
BP = T x 2πN = 200 x 2π x 2500/60 = 52.36 kW

MEP = BP/Vd
Vd = BP/MEP = 52.36/(750 x 10^3) = 6.98 x 10^-5 m^3

Vd = π/4 x D^2 x L
D = L
Vd = π/4 x D^2 x D = π/4 x D^3
D^3 = 4Vd/π = 4 x 6.98 x 10^-5/π
D = 0.392 m = 39.2 cm

Engine Capacity = Vd x Number of Cylinders = 6.98 x 10^-5 x 4 = 2.79 x 10^-4 m^3 = 3332 cc

Therefore, the engine capacity is 3332 cc (Option D).
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