Question

A diesel engine has cut-off ratio is $2$ and cut-off takes place at $5$% of the stroke. The air standard efficiency is ____ % Assume, $\gamma =1.4$

• A. 65.36

Answer 1

The correct option is A 65.36

$\frac{V_3}{V_2}=r_c=2$

$V_3=V_2+o.o5\times V_s$

$(V_5-V_2)=0.05\times (V_1-V_2)$

$(\frac{V_3}{V_2}-1)=0.05(\frac{V_1}{V_2}-1)$

$(2-1)=\left(0.05\right)(r-1)\text{(where r is compression ratio)}$

$=\frac{V_1}{V_2}$

We know that,

$\eta =1-\frac{1}{(r{)}^{\gamma -1}}\frac{\left(r_c^{\gamma -1}\right)}{\gamma (r_c-1)}$

$=1-\frac{1}{(21{)}^{1.4-1}}\frac{(2^{1.4}-1)}{1.4(2-1)}=0.6536=\mathrm{65..36}\%$