In a trial of single cylinder diesel engine the following observation were made: calorific value of fuel =43890 KJ/kg, Oil consumption = 10.2 kg/h, Speed=1900 rpm, Air consumption= 3.8 kg/min, compression ratio=15, Torque = 186 Nm, Quantity of cooling water used = 15.5 kg/min, Temp. Rise= 36oC, exhaust gas temp = 410oC, Room temp. = 20oC, Cp of exhaust gases = 1.17 KJ/kgK

Calculate: i) B.P. ii) BSFC iii) Heat Balance sheet on minute basis.

$$BP = \frac{{2\pi NT}}{{1000}} = \frac{{2\pi \times 1900 \times 186}}{{1000 \times 60}} = 37.01KW$$$$BSFC = \frac{{{m_f}}}{{BP}} = \frac{{10.2}}{{37.1}} = 0.2702Kg/KWhr$$ Heat balance sheet:

Heat supplied per minute $$ = \frac{{10.2 \times 43890}}{{60}} = 7461.3KJ/Min$$ Heat in BP: $$ = 37.01 \times 60 = 2220.6KJ/\min $$ Heat in cooling water: $$ = \frac{{15.5 \times 36 \times 4.2}}{1} = 2343.6KJ/\min $$ Heat in dry exhaust gases: ${Q_g} = Heat{\text{ taken by gases leaving the calorimeter}}$ $$ = {C_{pg}}{m_g}({T_g} - {T_a})$$ $${m_g} = {m_a} + {m_f} = {m_f}\left( {\frac{{{m_a}}}{{{m_f}}} + 1} \right) = \frac{{10.2}}{{60}}\left( {\frac{{3.8 \times 60}}{{10.2}} + 1} \right) = 3.97Kg/\min $$ $$ = 1.17 \times 3.97 \times \left( {410 - 20} \right)$$ $${Q_g} = 1811.511KJ/\min $$ Unaccounted Heat: $$ = {Q_s} - \left( {{Q_w} + {Q_{BP}} + {Q_g}} \right) = 7461.3 - \left( {2220 + 2343 + 1811.511} \right)$$ $$ = 1086.789KJ/\min $$