A diesel engine with CR= 20 has inlet at 520R, a maximum pressure of 920 psia and maximum temperature of 3200 R. With cold air properties find the cutoff ratio, the expansion ratio v4/v3, and the exhaust temperature.

Respuesta :

Answer:

Cut-off ratio[tex]\dfrac{V_3}{V_2}=6.15[/tex]

Cxpansion ratio[tex]\dfrac{V_4}{V_3}=3.25[/tex]

The exhaust temperature[tex]T_4=1997.5R[/tex]

Explanation:

Compression ratio CR(r)=20

[tex]\dfrac{V_1}{V_2}=20[/tex]

[tex]P_2=P_3=920 psia[/tex]

[tex]T_1=520 R ,T_{max}=T_3,T_3=3200 R[/tex]

We know that for air γ=1.4

If we assume that in diesel engine all process is adiabatic then

[tex]\dfrac{T_2}{T_1}=r^{\gamma -1}[/tex]

[tex]\dfrac{T_2}{520}=20^{1.4 -1}[/tex]

[tex]T_2=1723.28R[/tex]

[tex]\dfrac{V_3}{V_2}=\dfrac{T_3}{T_2}[/tex]

[tex]\dfrac{V_3}{V_2}=\dfrac{3200}{520}[/tex]

So cut-off ratio[tex]\dfrac{V_3}{V_2}=6.15[/tex]

[tex]\dfrac{V_1}{V_2}=\dfrac{V_4}{V_3}\times\dfrac{V_3}{V_2}[/tex]

Now putting the values in above equation

[tex]\dfrac20=\dfrac{V_4}{V_3}\times 6.15[/tex]

[tex]\dfrac{V_4}{V_3}=3.25[/tex]

So expansion ratio[tex]\dfrac{V_4}{V_3}=3.25[/tex].

[tex]\dfrac{T_4}{T_3}=(expansion\ ratio)^{\gamma -1}[/tex]

[tex]\dfrac{T_3}{T_4}=(3.25)^{1.4 -1}[/tex]

[tex]T_4=1997.5R[/tex]

So the exhaust temperature[tex]T_4=1997.5R[/tex]

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