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Bacteria growing in a batch reactor utilize a soluble food source (substrate) as depictedin Fig.P28.16. The up take of the substrate is represented by a logistic model with Michaelis-Menten limitation. Death of the bacteria produces detritus which is subsequently converted to the substrate by hydrolysis. In addition, the bacteria also excrete some substrate directly. Death, hydrolysis, and excretion are all simulated as first-order reactions. Mass balances can be written as
where X, C and
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Chapter 28 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
- 2. An electric heater is used to heat a slab, and the following model has been derived to predict the slab temperature: dT C3Q(t)- a(T – T) dt %3D | where T is the slab temperature in °R, Q(t) is the rate of heat input in Btu/h which is an input variable, C = 250 Btu/ºR, Ts = 530°R and a = 5x10-8 Btu/h-°R*. %3D %3D %3D (a) Obtain a linearized model around a slab steady state temperature of 650°R. (b) Obtain the transfer function for the process relating the slab temperature to the heating rate. Determine the time constant and steady state gain of the linearized model.arrow_forward2. An example of a linear decreasing model could be inventory in a warehouse that ships the same number of items each day. We will assume that this warehouse is going out of business, so no new calculators are being sent to the warehouse. Calculators in warehouse Calculators sold per day number of calculators sold per salesperson per day salespeople 2(a). Notice that this model has additional components shown as converters. Based on the titles of the converters, write the equation that must have been used to calculate the flow value in this model. Be sure to include appropriate units. Set the initial number of calculators to 10,000 {calculators}. If nnd that they each sell 15 modelarrow_forwardProblem 2. A linearized state space model of a three blade speed wind turbine with a 15 m radius working at 12 m/s wind-speed and generating 220 V is -5 5 1 -10.5229 -1066.67 -3.38028 23.5107 993.804 3.125 -23.5107 Wgm 10 -10 Wgm y = [ 0 0 0 1.223 × 10° 0] Wgm where 3 is the pitch angle of the wind turbine blades, { is the relative angle of the sec- ondary shaft, i is the angular velocity of the secondary shaft, wg is the generator speed, Wgm is the generator measurement speed, u is the pitch angle reference, and y is the active power generated. (a) What is the maximum number of poles that the transfer function could have? How many poles does it have?arrow_forward
- yo 9:1V i %A LO äbä 20 A ladder 13 ft long is leaning against a wall. The bottom of the ladder is being pulled away from the wall at the constant rate of 6 ft/min. How fast is the top of the ladder moving down the wall when the bottom of the * ?ladder is5 ft from the wall 13 y 6 ft/min 2.5 3.5arrow_forwardWhich of the following is not part of the transportation algorithm? Select one: a. northwest corner rule b. portfolio selection c. balanced transportation table d. stepping-stone methodarrow_forwardnumber 1 A food product containing 80% moisture content is being frozen. Estimate the specific heat of the product at -8 ° C when 80% of the water is frozen. The specific heat of the dry product is 2 kJ / (kg ° C). It is assumed that the specific heat of water at -10 ° C is the same as the specific heat of water at 0 ° C, and that the specific heat of ice follows the function Cp es = 0.0062 T Frozen + 2.0649. Cp of frozen product = kJ / kg ° C.arrow_forward
- The simple dynamic method is used to measure kļa in a fermenter operated at 30 C and 1 atm pressure. Data for the dissolved oxygen concentration as a function of time during the reoxygenation step are as follows: Time (s) CAL (% air saturation) 10 43.5 15 53.5 20 60.0 30 67.5 40 70.5 50 72.0 70 73.0 100 73.5 130 73.5 (a) Calculate the value of kla.arrow_forwardIn a linear finite element model related to bar problem in static equilibrium, as per the finite element model’s sign convention, which one of the following statements is true? Select one: a. If ue1 is negative then node 1 is moving to the right b. If ue1 is positive then node 1 is moving to the left c. If ue2 is negative then node 2 is moving to the left d. If ue2 is positive then node 2 is moving to the leftarrow_forwardthermal cycle simulation with Matlab, By integrating a turbocharger, a swirler combustor will be studied, designed and built for a hydrogen and ammonia fuelled engine which can work as a range extender for net zero vehicles.arrow_forward
- Q1/ Three reactors linked by pipes. As indicated, the rate of transfer of chemicals through each pipe is equal to a flow rate (Q, m³/s) multiplied by the concentration of the reactor from which the flow originates (C, mg/m³). In steady state, develop mass balance equations for the reactors, and solve the three simultaneous linear algebraic equations for their concentrations by Gauss-elimination method with partial pivoting. 400 mg/s 221%2 Q1301 1241 2 Q23c₂ 3 licz 200 mg/s 233 = 120 13 = 40 12 = 80 23 = 60 21 = 20arrow_forward16:57 A O * l LTE2 i ethuto.cut.ac.za/webapps/asse 27 ¥ Question Completion Status: QUESTION 53 The following processes occurs in a reversible thermodynamic cycle: 1-2: Reversible polytropic compression at pressure 0.6 bar at volume 0.08 m3 to a pressure 10.2 bar and specific volume 0.4 m3/kg. The index of compression may be taken as n. 2-3: Reversibly expansion with expansion index of 2 to pressure 3 bar. 3-1: Reversible cooling at constant volume to the initial state. Calculate the value of n in the process to 3 decimal places. Click Save and Submit to save and submit. Click Save All Answers to save all answers. Save All Answers Close Window Save and Submitarrow_forwardGiven: Consider an adiabatic steam turbine operating at steady-flow conditions. The known operating conditions are: Inlet conditions Exit (outlet) conditions Pressure (MPa) Temperature (°C) Velocity (m/s) Steam quality Mass flow rate (kg/s) Elevation (height) (m) 10 450 0.010 80.01 50.01 91.9 % 12.01 9.0 9.0 Required: Draw clear and consistent schematic for the problem representing the inlet and exit (outlet) conditions and label your schematic with the given conditions. Analyze the problem systematically using step-by-step CV energy and mass analyses, justify the equations, state your assumptions, and determine the following (circle your final answers): (a) The specific enthalpy values at inlet and exit of the turbine. (b) The mass flow rate of steam at exit. (c) The specific heat transfer. (d) The rate of change in the kinetic energy of the steam between inlet and exit. (e) The power output generated by the turbine. (f) The specific work output. (g) The specific volumes at inlet and…arrow_forward
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