Answer to Question #183631 in Mechanical Engineering for randz

Question #183631

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.


1
Expert's answer
2021-04-22T07:23:08-0400

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"

Wnet

"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"


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