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```"given"

P[6]=7000[KPa]
T[6]=500[C]
P[7]=600[KPa]
P[8]=10[KPa]
m_dot=30[kg/s]
m_frac=0.25
Fluid\$ = 'Steam_IAPWS'

"mass balance"

m_dot[7]=m_frac*m_dot

m_dot[3]=m_dot[7]

m_dot[8]=(1-m_frac)*m_dot

m_dot[1]=m_dot[8]

m_dot[2]=m_dot[1]

m_dot[4]=m_dot

m_dot[5]=m_dot

m_dot[6]=m_dot

"pump I"

P[1]=P[8]

P[2]=P[7]

w_p1_in = v[1] * (P[2]-P[1])

v[1]= volume(Fluid\$, P=P[1], x=0)

h[1]= enthalpy(Fluid\$, P=P[1], x=0)

h[2] =h[1] + w_p1_in

"mixing chamber "

P[3] = P[7]

h[3] = enthalpy(Fluid\$,P=P[3], x=0)

m_dot[4] * h[4] = m_dot[2] * h[2] + m_dot[3] * h[3]

"pump II"

v[4] = volume(Fluid\$, h=h[4], x=0)

P[4]=P[7]

P[5]=P[6]

w_p2_in = v[4]*(P[5]-P[4])

h[5] = h[4] + w_p2_in

"turbine"

h[6] = enthalpy(Fluid\$,P=P[6], T=T[6])

s[6] = entropy(Fluid\$,P=P[6], T=T[6])

s[7]=s[6]

h[7]=enthalpy ( Fluid\$,P=P[7], s=s[7])

s[8]=s[6]

h[8]=enthalpy ( Fluid\$,P=P[8], s=s[8])

x[8]=quality(Fluid\$,P=P[8],s=s[8])

"energy balance"

Q_out_ph= m_dot[7] * (h[7] - h[3])

Q_in_b= m_dot[5] * (h[6] - h[5])

W_in_p= (m_dot[1] * w_p1_in) + (m_dot[4] * w_p2_in)

W_out_t = m_dot[7]*(h[6]-h[7]) + m_dot[8]*(h[6]-h[8])

W_out_net = (W_out_t) - (W_in_p)

epsilon_u = (W_out_net  + Q_out_ph) / Q_in_b```