Answer to Question #177045 in Mechanical Engineering for Micheal Vaughn

Question #177045

Simple two stage (effect) parallel flow multi-effect evaporation unit with vapour compression A two-effect thermal vapor-compression system is designed at the following operating conditions: Motive steam ms: Ps: Ts mm; Pm Tm Feed water mf 1 mt2 Cooling Sea water md2 mev: Pev: Tev Demiater (1) (2) Intake Heating Sea water Steam mm md1 Down condenser md2-mev md Distillate Condensate mb 1 mb2 mb Rejected brine mev The areas of the exchangers are equal: Ae1=Ae2 - Boiling temperatures, T61= 75°C; Tb2, of 70°C; Feed water temperature; T= 65°C. - Motive steam pressure, Pm = 800 kPa. - Brine reject concentration, Xb= 60,000 ppm; Intake seawater salinity, Xp = 30,000 ppm - Intake seawater temperature, Tcw = 15°C System capacity, ma= 1 kg/s Determine the specific heat transfer area, the entrainment ratio, and the flow rates of: entrainment vapor; motive steam; supply steam and cooling water, and the performance ratio.


1
Expert's answer
2021-04-01T01:11:49-0400

As per the data

"Q_s=mc_p \\triangle T"

Stream mass flow rate "\\frac{Q_s}{C_p \\triangle T}= \\frac{8000}{4.2 \\times(75-70)}=142.85 kg\/s"

"Q_s=Q_k"

"mC_p \\triangle T=mC_p \\triangle T"

Specific heat of sea water = 3.85 kg/s

"m_s C_{p_s} \\triangle T=m_cC_{p_c} \\triangle T"

"m_c= \\frac{m_s C_{p_s} \\triangle T}{C_{p_c} \\triangle T}= \\frac{142.85 \\times4.2 \\times (75-70)}{3.85 \\times(65-15)}=15.58 kg\/s"


"Q_s=3000kW ; T_{cw}=15^OC; T_{b1}=75^oC; T_{b2}=70^oC; T_F=65^oC"

"x_f=35000, x_b=30000"

"A_{e1}=A_{e2}"

"U_{e1}=U_{e2}=2.25 kW\/m^{2 \\space o}C"

"U_{c}=1.9 kW\/m^{2 \\space o}C"

"C_p=4.2"


"\\triangle T_1=75-15=60^oC"

"\\triangle T_2=70-65=5^oC"

"\\triangle TIn(\\triangle T_1-\\triangle T_2)= \\frac{60.5}{In \\frac{60}{5}}=22.16 ^oC"

"U=2.25 kW\/m^{2 \\space o}C=2250 W\/m^{2 \\space o}C"

"Q=UA\\triangle TIn(\\triangle T_1-\\triangle T_2)"

"A = \\frac{Q}{U\\triangle TIn(\\triangle T_1-\\triangle T_2) }= \\frac{8000}{2.250 \\times 22.13}=60.25 m^2"


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