Question

An ideal diesel engine has a diameter (bore) of 15 cm and stroke 20 cm. The clearance volume is 10 percent of the swept volume. If the cut-off takes place at 5 percent of the stroke, the air standard efficiency of the engine is _____%.

• A. 58.168

Answer 1

The correct option is A 58.168
$D=15cm;L=20cm;V_s=\frac{\pi }{4}(D{)}^{2}L=\frac{\pi }{4}(15{)}^2\times 20=3534c{m}^3$


$V_c=0.1V_s=353.4c{m}^3$

$r=1+\frac{V_s}{v_c}=1+\frac{V_s}{0.1v_s}=11$

$V_3-V_2=$ 5% of $V_s$

$\rho =\frac{V_5}{V_2}=\frac{V_2+(V_3-V_2)}{V_2}=\frac{V_c+0.05V_S}{V_C}=\frac{353.4+0.05\times 3534}{353.4}=1.5$

$n_{diesel}=1-\frac{1}{{\gamma }^{1.4-1}}\left[\frac{{\rho }^{1.4}-1}{1.4(\rho -1)}\right]$

$=1-\frac{1}{(11{)}^{0.4}}\left[\frac{{1.5}^{1.4}-1}{1.4(1.5-1)}\right]=0.58168$

$\Rightarrow n_{diesel}=$ 58.168%