Mean effective pressure in a diesel engine

[Monsterboy]

Homework Statement

Air enters a diesel engine with a density of 1.0 kg/m³. The compression ratio is 21 .At steady state ,the air intake is 30 x10^-3 Kg/s and the net work output is 15 kW .The mean effective pressure (in kPa) is ...

Homework Equations

P_m= W.D/ V_s
C = V₁/V₂
V₁ =V_s +V_c
V₂=V_c

$\eta$ = 1- $\frac{1}{r^(\gamma-1)} \frac{ \rho^\gamma-1}{(\rho-1)\gamma}$
P_m -mean effective pressure
W.D -work done
V_s -stroke volume
V_c-clearance volume
$\gamma$ -ratio of specific heats.
$\rho$ -density (rho)
$\eta$ -efficiency (eta)
Mass flow rate -m^.
C- compression ratio

The Attempt at a Solution

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Since density is 1 kg/m³ ,the efficiency becomes 100% according to the formula.
because there is a (rho-1) term in the denominator of the second term.

If the above is correct then W.D =Heat supplied = 15kW

So m^. /density = Volume flow rate = V_s ?

if r= 21 ,then V_s =20V_c

So volume flow rate = 30x10^-3 = V_s ?

So mean effective pressure =15000W/(30x10^-3)
= 500 kPa
Is the above calcualtion correct ?
but the answer given to me is 525 kPa

 

[Monsterboy]

I just want to know whether my calculation is right because i am not getting the answer i was given.

 

[Monsterboy]

Oops! rho is not density , it is cut-off ratio.