Willian’s line test is conducted on a constant speed diesel engine operating at 1500 rpm and developing 50 KW power output at full load. Willan’s line may be considering as a straight line up to 60% load, with the slope of the line being 8° (eight degrees). The fuel consumption for this engine is 2.46kg/h at 10% load. Calorific value (C.V.) of fuel used is 42MJ/kg. Calculate (i) Frictional power (ii) Fuel consumption in kg/h at 60% load (iii) Brake thermal efficiency at 60% load. (iv) Mechanical efficiency at 40% load (v) Brake torque at 40% load.

N = rpm,

B.P.(at full load) = 50 kW

Slope of William’s line = 8°

Mf at 10% load = 2.46 Kg/hr

C.V.= 42 MJ/kg

(i) Frictional Power (F.P.):

The negative intercept (x) on X-axis represents the F.P.

10% of Load = 0.1 X B.P. at full load = 0.1 X 50 = 5 kW

10% of Load = 0.4 X 50 = 20 kW

10% of Load = 0.6 X 50 = 30 kW

By measurements, mf at B – 3.15 kg/hr = BD and mf at F = 2.6 kg/hr = SF

Consider similar ∆s ABC and EDB,

(ii) Fuel consumption at 60% load: = 3.15 kg/hr (from above)

(iii) Brake Thermal Efficiency at 60% load i.e. at B.P. = 30kW:

(iv) Mechanical Efficiency at 40% load i.e. at B.P. = 0.4 X 50 = 20kW:

(v) Brake torque,T at 40% load i.e. at B.P. = 20kW :