A shell-and-tube heat exchanger is to be used to cool 200,000 lb/h (25.2 kg/s) of water from 100?F (38?C) to 90?F (32?C). The exchanger has one shell-side pass and two tube side passes. The hot water flows through the tubes and the cooling water flows through the shell. The cooling water enters at 75?F (24?C) and leaves at 90?F (32?C). The shellside (outside) heat transfer coefficient is estimated to be 1000 Btu/(h ft2 ?F) (5678W/(m2 K)). Design specifications require that the pressure drop through the tubes be as close to 2 psi (13.8 kPa) as possible and that the tubes be 18 BWG copper tubing (1.24 mm wall thickness), and each pass is 16 feet (4.9 m) long. Assume that the pressure losses at the inlet and outlet are equal to one and one half of a velocity heat (ρV2/gc), respectively. For these specifications, what tube diameter and how many tubes are needed?GIVENA water-to-water shell-and-tube exchanger, hot water in tubes, cooling water in shellOne shell and two tube passesHot water flow rate (mh) = 25.2 kg/sWater temperaturesHot: Th,in = 38?C Th,out = 32?CCold: Tc,in = 24?C Tc,out = 32?CShell-side transfer coefficient (ho ) = 5678 W/(m2 K)Pressure drop (??p) = 13.8 kPaTube wall thickness (t) = 1.24 mm = 0.00124 mTube length per pass (Lp) = 4.9 mASSUMPTIONSPressure losses at inlet and outlet (??pii) = 1.5 (ρV2/gc)Variation of thermal properties with temperature is negligibleFouling resistance is negligibleThermal resistance of the tube walls isnegligible

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Coollng Water Tạh= 24°C Thout - 32°C Hot Thn= 38°C Water Teout = 32°C