# Example 11.1 Pc = 10.0 kPa Pb = 2.0 Mpa n = 0.00101 kJ/kg/kPa wp = n * (Pb - Pc) ; kJ/kg h1 = 191.8 kJ/kg h2 = h1 + wp ; kJ/kg h3 = 2799.5 kJ/kg qh = h3 - h2 ; kJ/kg s3 = 6.3409 kJ/kg/degK s4 = s3 ; kJ/kg/degK sf = 0.6493 kJ/kg/degK sfg = 7.5009 kJ/kg/degK x4 = (s4 - sf) / sfg hfg = 2392.8000 kJ/kg h4 = h1 + x4 * hfg ; kJ/kg wt = h3 - h4 ; kJ/kg qL = h4 - h1 ; kJ/kg hth = (wt - wp) / qh # Example 11.2 P1 = 4.0 Mpa T1 = 400.0 degC P2 = 10.0 kPa n = 0.00101 kJ/kg/kPa wp = n * (P1 - P2) ; kJ/kg h1 = 191.8 kJ/kg h2 = h1 + wp ; kJ/kg h3 = 3213.6 kJ/kg qh = h3 - h2 ; kJ/kg s3 = 6.7690 kJ/kg/degK s4 = s3 ; kJ/kg/degK sf = 0.6493 kJ/kg/degK sfg = 7.5009 kJ/kg/degK x4 = (s4 - sf) / sfg hfg = 2392.8000 kJ/kg h4 = h1 + x4 * hfg ; kJ/kg wt = h3 - h4 ; kJ/kg hth = (wt - wp) / qh qL = h4 - h1 ; kJ/kg wnet = qh - qL ; kJ/kg # Example 11.2E P1 = 600.0 psi T1 = 800.0 degF P2 = 1.0 psi n = 0.00101 kJ/kg/kPa wp = n * (P1 - P2) ; Btu/lbm h1 = 69.7 Btu/lbm h2 = h1 + wp ; Btu/lbm h3 = 1407.0 Btu/lbm qh = h3 - h2 ; Btu/lbm s3 = 1.6343 Btu/lbm/degR s4 = s3 ; Btu/lbm/degR sf = 1.9779 Btu/lbm/degR sfg = 1.8453 Btu/lbm/degR x4 = (sf - s4) / sfg hfg = 1105.8000 Btu/lbm hf = 1036.0000 Btu/lbm h4 = hfg - x4 * hf ; Btu/lbm wt = h3 - h4 ; Btu/lbm hth = (wt - wp) / qh qL = h4 - h1 ; Btu/lbm wnet = qh - qL ; Btu/lbm # Example 11.3 P1 = 4.0 Mpa T1 = 400.0 degC P2 = 400.0 kPa T3 = 400.0 degC P4 = 10.0 kPa h3 = 3213.6 kJ/kg s3 = 6.7690 kJ/kg/degK s4 = s3 ; kJ/kg/degK sf = 1.7766 kJ/kg/degK sfg = 5.1193 kJ/kg/degK x4 = (s4 - sf) / sfg hf = 604.7000 kJ/kg hfg = 2133.8000 kJ/kg h4 = hf + x4 * hfg ; kJ/kg h5 = 3273.4 kJ/kg s5 = 7.8985 kJ/kg/degK s6 = s5 ; kJ/kg/degK sf = 0.6493 kJ/kg/degK sfg = 7.5009 kJ/kg/degK x6 = (s6 - sf) / sfg hf = 191.8000 kJ/kg hfg = 2392.8000 kJ/kg h6 = hf + x6 * hfg ; kJ/kg wt = (h3 - h4) + (h5 - h6) ; kJ/kg n = 0.00101 kJ/kg/kPa wp = n * (P1 - P2) ; kJ/kg h1 = 191.8 kJ/kg h2 = h1 + wp ; kJ/kg qH = (h3 - h2) + (h5 - h4) ; kJ/kg hth = (wt - wp) / qH ## Example 11.4 # P4 = 4.0 Mpa # T4 = 400.0 degC # P2 = 400.0 kPa # P3 = 400.0 kPa # P1 = 10.0 kPa # n = 0.00101 kJ/kg/kPa # wp = n* (P2 - P1) ; kJ/kg # h1 = 191.8 kJ/kg # h2 = h1 + wp ; kJ/kg # h3 = 604.7 kJ/kg # h6 = 2685.6 kJ/kg # m1 = 0.16544 kg # err1 = h3 # err2 = m1 * h6 # err3 = (1.0 kg - m1) * h2 # h5 = 3213.6 kJ/kg # h7 = 2144.1 kJ/kg # wt1 = (h5 - h6) # wt2 = (1.0 kg - m1)* (h6 - h7) # wt = wt1 + wt2 # n2 = 0.0010840 kJ/kg/kPa # wp2 = n2 * (P4 - P3) ; kJ/kg # h4 = h3 + wp2 ; kJ/kg # wnet1 = wt1 - wt2 # wnet2 = (1.0 kg - m1) * wp # wnet3 = wp2 # qH = h5 - h4 ; kJ/kg # hth = wnet / qh # Example 11.5 h5 = 3169.1 kJ/kg s5 = 6.7235 kJ/kg/degK s6 = s5 ; kJ/kg/degK sf = 0.6493 kJ/kg/degK sfg = 7.5009 kJ/kg/degK x6 = (s6 - sf) / sfg hf = 191.8000 kJ/kg hfg = 2392.8000 kJ/kg h6 = hf + x6 * hfg ; kJ/kg ht = 0.8600 wt = ht * (h5 - h6) ; kJ/kg P1 = 10.0 kPa P2 = 5.0 Mpa n = 0.0010090 kJ/kg/kPa hp0 = 0.80 wp = n* (P2 - P1) / hp0 wnet = wt - wp ; kJ/kg h4 = 3213.6 kJ/kg h3 = 171.8 kJ/kg qH = h4 - h3 ; kJ/kg hth = wnet / qH # Example 11.5E h5 = 1386.8 Btu/lbm s5 = 1.6248 Btu/lbm/degR s6 = s5 ; Btu/lbm/degR sf = 1.9779 Btu/lbm/degR sfg = 1.8453 Btu/lbm/degR one_minus_x6 = (sf - s6) / sfg hf = 1105.8000 Btu/lbm hfg = 1036.0000 Btu/lbm h6 = hf - one_minus_x6 * hfg ; Btu/lbm ht = 0.8600 wt = ht * (h5 - h6); Btu/lbm P1 = 1.0 psi P2 = 800.0 psi n = 0.0010090 kJ/kg/kPa hp0 = 0.80 wp = n * (P2 - P1) / hp0 ; Btu/lbm wnet = wt - wp ; Btu/lbm h4 = 1407.6 Btu/lbm h3 = 65.1 Btu/lbm qH = h4 - h3 ; Btu/lbm hth = wnet / qH # Example 11.6 T1 = 15.0 degC P1 = 0.1 Mpa P2 = 1.0 Mpa Tmax = 1100.0 degC Tg = 300.0 degK k = 1.4 T2_over_T1 = (P2 / P1)^((k-1)/k) T2 = T1 *T2_over_T1 ; degC Cp = 1.004 kJ/kg/degK wc = Cp * (T2 - T1) ; kJ/kg P3 = P2 ; kPa P4 = P1 ; kPa T3_over_T4 = (P3 / P4)^((k-1)/k) T3= Tmax ; degC T4 = T3 / T3_over_T4 ; degC qH = Cp * (T3 - T2) ; kJ/kg qL = Cp * (T4 - T1) ; kJ/kg wnet = qH - qL ; kJ/kg hth = wnet / qH hth = 1 - 1 / (P2 / P1)^((k-1)/k) # Example 11.7 T1 = 15.0 degC P1 = 0.1 Mpa P2 = 1.0 Mpa Tmax = 1100.0 degC hc = 0.80 ht = 0.85 DP = 15.0 kPa Tg = 300.0 degK k = 1.4 e = (k - 1) / k T2s = T1 * (P2 / P1)^e ; degC T2 = T1 + (T2s - T1) / hc ; degC Cp = 1.004 kJ/kg/degK wc = Cp * (T2 - T1) ; kJ/kg P3 = P2 - DP ; kPa P4 = P1 ; kPa T4s = Tmax / (P3 / P4)^e ; degC T4 = Tmax - ht * (Tmax - T4s) ; degC wt = Cp * (Tmax - T4) ; kJ/kg wnet = wt - wc ; kJ/kg qH = Cp * (Tmax - T2) ; kJ/kg hth = wnet / qH # Example 11.8 T3 = 1100.0 degC Tx = 710.8 degK Cp = 1.004 kJ/kg/degK qH = Cp * (T3 - Tx) ; kJ/kg wnet = 395.200 kJ/kg hth = wnet / qH # Example 11.9 R = 0.2870 kJ/kg degK Ti = 15.0 degC Pi0 = 0.1 Mpa Pe = 1.0 Mpa w = -R * Ti * ln(Pe / Pi0) ; kJ/kg Tt = 1100.0 degC wt = -R * Tt * ln(Pi0 / Pe) ; kJ/kg # Example 11.10 P1 = 0.10 Mpa T1 = 15.0 degC P2 = 1.00 Mpa T2 = 283.5 degC wc = 269.5 kJ/kg P3 = 1.00 Mpa T3 = 1100.0 degC Cp = 1.004 kJ/kg/degK wc = Cp * (T2 - T1) ; kJ/kg wt = wc ; kJ/kg T4 = T3 - wc / Cp ; degC k = 1.4 e = (k - 1) / k P4 = P3 / (T3 / T4)^(k/(k-1)) ; Mpa P5 = 0.10 Mpa T5 = 710.8 degK V0 = sqrt(2 * Cp * (T4 - T5)) ; m/s # Example 11.11 rv = 10.00 P1 = 0.10 Mpa T1 = 15.0 degC qH = 1800.0 kJ/kg R = 0.2870 kJ/kg degK n1 = R * T1 / P1 ; m^3/kg k = 1.4 T2 = T1 * rv^(k-1) ; degC P2 = P1 * rv^k ; Mpa n2 = n1 / rv ; m^3/kg Cv = 0.7 kJ/kg/degK T3 = T2 + qH / Cv ; degC P3 = P2 * (T3 / T2) ; Mpa T4 = T3 / rv^(k-1) ; degC P4 = P3 / rv^k ; Mpa hth = 1 - 1 / rv^(k-1) q41 = Cv * (T1 - T4) ; kJ/kg hth = 1 + q41 / qH wnet = qH + q41 ; kJ/kg mep = wnet / (n1 - n2) ; kPa # Example 11.12 rv = 20.00 qH = 1800.0 kJ/kg P1 = 0.10 Mpa T1 = 15.0 degC R = 0.2870 kJ/kg degK n1 = R * T1 / P1 ; m^3/kg n2 = n1 / rv ; m^3/kg k = 1.4 T2 = T1 * rv^(k-1) ; degC P2 = P1 * rv^k ; Mpa Cp = 1.004 kJ/kg/degK T3 = T2 + qH / Cp ; degC n3 = 0.11896 m^3/kg T4 = T3 / (n1 / n3)^(k-1) ; degC Cv = 0.717 kJ/kg/degK qL = Cv * (T1 - T4) ; kJ/kg wnet = qH + qL ; kJ/kg hth = wnet / qH mep = wnet / (n1 - n2) ; kPa # Example 11.13 T1 = -20.0 degC T3 = 40.0 degC mdot = 0.030 kg/s Pg_T3 = 1017.00 kPa P2 = Pg_T3 h1 = 386.1 kJ/kg s1 = 1.7395 kJ/kg/degK s2 = s1 ; kJ/kg/degK T2 = 47.7 degC h2 = 428.4 kJ/kg wc = h2 - h1 ; kJ/kg h4 = 256.5 kJ/kg h3 = h4 qL = h1 - h4 ; kJ/kg b = qL / wc Capacity = qL * mdot ; kW # Example 11.14 T1 = -10.0 degC P1 = 0.125 Mpa T2 = 100.0 degC P2 = 1.2 Mpa T3 = 80.0 degC P3 = 1.19 Mpa T4 = 45.0 degC P4 = 1.160 Mpa T5 = 40.0 degC P5 = 1.150 Mpa P7 = 0.140 Mpa P6 = P7 T8 = -20.0 degC P8 = 0.130 Mpa qH = 4.0 kJ/kg h1 = 185.2 kJ/kg h2 = 245.5 kJ/kg wc = h2 - h1 + qH ; kJ/kg h7 = 74.5 kJ/kg h6 = h7 h5 = h6 h8 = 179.1 kJ/kg qL = h8 - h7 ; kJ/kg b = qL / wc # Example 11.14a T1 = -20.0 degC P1 = 0.100 Mpa P2 = 0.5 Mpa T3 = 15.0 degC k = 1.4 T2 = T1 * (P2 / P1)^((k-1) / k) ; degC Cp = 1.004 kJ/kg/degK wc = Cp * (T2 - T1) ; kJ/kg P3 = P2 ; Mpa P4 = P1 ; Mpa T4 = T3 / (P2 / P1)^((k-1) / k) ; degC wt = Cp * (T3 - T4) ; kJ/kg qH = Cp * (T2 - T3) ; kJ/kg qL = Cp * (T1 - T4) ; kJ/kg wnet = wc - wt ; kJ/kg b = qL / wnet Qdot = 1.000 kW mdot = Qdot / qL ; kg/s # Homework Problems: TBD