ENVIRONMENTAL ENGINEERING - QUESTION 22.3 : A well delivers 225 US-gallons per minute of water to a chemical plant during normal system operation. (a) Calculate its flowrate in the unit of mega US-gallon per day or MGD. (b) The following formula is written next to the chlorine feed point : (chlorine feed rate, lb / day) = (flowrate, MGD) X (dose, mg / L) x (8.34). If this formula is correct, then what should the chlorine feed rate to be in pounds per day (lb / day) if the desired dose is 2 mg / L. (c) Prove by calculations that the constant 8.34 in the formula next to the chlorine feed point is correct. Let 1 US-gallon = 3.78541 L and 1 mg = 0.0000022046 pound.
ENVIRONMENTAL ENGINEERING - ANSWER 22.3 : (a) Flowrate = (225 US-gallon / minute) / [ (hour / 60 minute) x (day / 24 hour) ] = 324000 or 0.324 MGD. (b) Chlorine feed rate = 0.324 MGD x 2 mg / L x 8.34 = 5.40432 lb / day. (c) The constant is derived from 0.0000022046 pound / mg x 1000000 US-gallon / M US-gallon x 3.78541 L / US-gallon = 8.345 with minor error (proven). The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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In a Laplace Transform Table, the Laplace transfer function of f(t) is F(s). When d(t) = f(t) then 1 = F(s). When x(t) = f(t) then X(s) = F(s). If d(t) is the impulse of a spring when d(t) = kx(t), then derive the equation for the impulse of a spring as X(s) in term of k. Next question : A controller has a transfer function a and the other controller has a transfer function b. The overall transfer function of both controllers is ab. What is the transfer function overall when both controllers have similar transfer function 1 / (Cs k)?
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ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.12 : You, as an engineer, buy a piece of biochemical instrument to start a servicing business. The instrument has a useful life of 3 years, that costs $60k. The instrumental business generates $100k per year. The labor costs $50k per year. The $60k new instrument depreciates in its value evenly up to 3 years, thereafter the old instrument needs to be replaced by another piece of new instrument. (i) In the first year of this engineering business : (a) what is its starting cash? (b) calculate the depreciation value of the instrument. (c) find the operating profit generated. (d) what is the capital expense of the business? (e) calculate the cash from operation. (f) calculate the ending cash. (ii) Based on the income statement of the business in the second year : (a) find the capital expense of the business. (b) what is its starting cash? (c) calculate the depreciation value of the instrument. (d) find the operating profit generated. (e) calculate the cash from operation. (f) calculate the ending cash.
QUANTUM BIOLOGY - EXAMPLE 33.7 : (a) In a DNA of a living cell, the quantum information available in the bases guanine (G) and thymine (T) are | G > = | 110 > and | T > = | 010 > respectively. Calculate | G > - | T >. (b) In a living biological cell, the step time for random walk of an electron is t. The localization time of an electron is T. If i is the geometric average of T and t, find log T as a function of t and i.
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Question 57 – There are 2 simultaneous equations : (A1) x + (B1) y = D1 and (A2) x + (B2) y = D2. (a) By using Excel program, find the values of x and y when A1 = 80, A2 = 150, B1 = 52, B2 = 100, D1 = 3.5 and D2 = 2.3. (b) Write the expression of Excel in the form of =MMULT(MINVERSE(W:X),Y:Z) in order to get the values of x and y. W, X, Y and Z may be A1, A2, B1, B2, D1 and D2.
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REACTION ENGINEERING - EXAMPLE 13.2 : A batch reactor is designed for the system of the irreversible, elementary liquid-phase hydration of butylene oxide that produces butylene glycol. At the reaction temperature T = 323 K, the reaction rate constant is k = 0.00083 L / (mol - min). The initial concentration of butylene oxide is 0.25 mol / L = Ca. The reaction is conducted using water as the solvent, so that water is in large excess. (a) Let the molecular weight of water is 18 g / mol and the mass of 1 kg in 1 L of water, calculate the molar density of water, Cb in the unit of mol / L. (b) Determine the final conversion, X of butylene oxide in the batch reactor after t = 45 min of reaction time. Use the formula X = 1 - 1 / exp [ kt (Cb) ] derived from material balance. (c) Find the equation of t as a function of X.
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