Question

4. There are supplied 320 KJ/cycle of Diesel engine operating on 250 g of air P 1 =97.91 KPa, T 1 =48.9C.

At the end of compression, P 2 =3930KPa. Assume that air and the product within the cycle have air

properties. Determine compresion ratio, cut-off ratio, Wnet, thermal efficiency, and mean effective

pressure.

Answer 1

Compression ratio

$r=\frac{v_1}{v_2}=(\frac{p_2}{p_1})^{1/\gamma}=(\frac{3930}{97.91})^{1/1.4}=13.97$

Cut-off ratio

$r_c=\frac{v_3}{v_2}=(\frac{T_3}{T_1})$

But $\frac{T_2}{T_1}=(\frac{v_2}{v_1})^{\gamma -1} \implies T_2=322.05(13.97)^{1.4-1}=924.7 K$

$320=0.25 \times1.005 \times(T_3-924.7) \implies T_3=2198.33184 K$

So, $r_c=(\frac{2198.33}{924.7})=2.4$

Thermal efficiency

$1-\frac{1}{r^{\gamma -1}}[\frac{1}{\gamma} \times \frac{r_c^{\gamma}-1}{r_c-1}]$

$1-\frac{1}{13.97^{1.4 -1}}[\frac{1}{1.4} \times \frac{2.4^{1.4}-1}{2.4-1}]=0.57240$

W_net

$0.57240 \times320=183.168 kJ/cycle$

Mean effective pressure.

$P_m=\frac{W_{net}}{V}=\frac{0.5724 \times 1.4 \times 3930 \times(2.4-1)}{(13.97-1)(1.4-1)}=849.86174 kPa$