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Unformatted text preview: A dt d ( Hx B ) = Fx F - Bx - Dx D B dt 3. Consider the stirred tank heater shown below (Figure 2). The steam is injected direct ly in the liquid water. A1 is the cross sect ional area of the tank. Assume that the effluent flow rate is proportional to the liquid static pressure that causes its flow. a) Ident ify the state variables of the system. b) Determine what balances you should perform. c) Develop the state model that describes the dynamic behavior of the system. Steam, 40 psi Q1 (kg/min) F1, T1 Water A, h F2, T2 Figure 2: Stirred tank heater Solution: a) State Variables: h , T2 b) Total mass and energy balance. Total mass balance accumulation input output =
time time time d ( rA h )
= rF - rF + Q 1
d t At constant densit y:
Total energy balance dh Q = F1 - F2 + dt r Equation 1 accumulation input output = time time time E = U + KE + PE , Where U is the internal energy, KE is the kinetic energy and PE is the potential energy. Since the tank is not moving, dKE dPE = = 0 . d t d t Thus dE dU = , d t d t and for liquid systems, dU dH T
= d t d t Where, HT is the total enthalpy of material in the tank. Total mass in the tank is rV = rAh . H may be written as, rAhC p (T - T ) ref Where Tref : is the reference temperature. The input of total...
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