Chapter 7, Problem 7.39P

(A)

Interpretation Introduction

Interpretation:

to find the number of stages

Concept Introduction:

Initial Pressure $P_1=1atm$

Initial temperature $T_1=(35+273.15)K$

$T_1=308.15$ K

Final pressure $P_2=50atm$

Outlet temperature $T_2=(200+273.15)K$

$T_2=473.15$ K

Efficiency, $\eta =0.65$

Volumetric flow rate $Vdot=0.5\frac{m^3}{\sec }$

$C_P=3.5\times R$

Assume air as ideal gas, $V=\frac{R\times T_1}{P_1}$

$ndot=\frac{Vdot}{V}$

(B)

Interpretation Introduction

Interpretation:

To calculate the mechanical power required per stage

Concept Introduction:

Initial Pressure $P_1=1atm$

Initial temperature $T_1=(35+273.15)K$

$T_1=308.15$ K

Final pressure $P_2=50atm$

Outlet temperature $T_2=(200+273.15)K$

$T_2=473.15$ K

Efficiency, $\eta =0.65$

Volumetric flow rate $Vdot=0.5\frac{m^3}{\sec }$

$C_P=3.5\times R$

$W_s(isentropic)=C_p{T}_1\left[{\left(\frac{P_2}{P_1}\right)}^{\frac{R}{C_p}}-1\right]$

(C)

Interpretation Introduction

Interpretation:

To calculate the heat duty for each intercooler

Concept Introduction:

Initial Pressure $P_1=1atm$

Initial temperature $T_1=(35+273.15)K$

$T_1=308.15$ K

Final pressure $P_2=50atm$

Outlet temperature $T_2=(200+273.15)K$

$T_2=473.15$ K

Efficiency, $\eta =0.65$

Volumetric flow rate $Vdot=0.5\frac{m^3}{\sec }$

$C_P=3.5\times R$

By first law

$Q_r=-W_r$

(D)

Interpretation Introduction

Interpretation:

To find the mass flow rate of cooling water per intercooler

Concept Introduction:

Take Energy balance on each interchanger