ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.4 : A university is enrolling new students of biochemical engineering degree. A long queue is formed during registration. Let L = rate of newcomers to a queue, m = number of clients served at a certain time, T = time in system. In M / M / 1 queue, let T = time waiting in a queue + service time, L = 2 / second, m = 3 / second. (a) Find the service time, A = 1 / m. (b) Calculate time waiting in a queue, B = A (L / m) / (1 - L / m). (c) What is the value of T?
ACCOUNTING AND FINANCIAL ENGINEERING - ANSWER 34.4 : (a) A = 1 / m = 1 / 3 second. (b) B = A (L / m) / (1 - L / m) = (1 / 3) (2 / 3) / (1 - 2 / 3) = 2 / 3 second. (c) T = A + B = 1 / 3 + 2 / 3 = 1 second. 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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UNIT OPERATION - EXAMPLE 9.4 : Acetone and ethanol are separated using a distillation column with a partial condenser and partial reboiler. An equimolar, sub-cooled liquid feed enters at 100 kmol / hr and condenses 1 mole of vapor for every 6 moles of feed. The separation requires a distillate vapor that is 95 mol % acetone and bottoms liquid that is 5 mol % acetone. The reflux is returned from the condenser to the column as a saturated liquid and the operation is run at (L / V) = 1.4 * (L / V) min. Assume constant overflow conditions. (a) Feed operating line is y = [ q / (q - 1) ] x - z / (q - 1) where z = 0.5 for equimolar liquid mixture of 2 components, q = (L'- L) / F where L' = L + F + (F / 6) for condensation of 1 mole of vapor / 6 moles of feed. What is y = f(x)? (b) The rectifying operating line is y = (L / V) x + (D / V) (xd) where (L / V) min goes through the points A (0.95, 0.95) and B (0.53, 0.69), V = L + D. What is y = f(x)? Let xd = 0.95. (L / V) min is the slope of the 2 points A and B.
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Calculate the cooling duty, H required to condense and cool acetone from 100 degree Celsius to 25 degree Celsius at atmospheric pressure. The heat of vaporization for acetone at its normal boiling point is 30.2 kJ / mol. The boiling point of acetone at atmospheric pressure is 56 degree Celsius. The flowrate of acetone through the condenser is 100 mol / s = N. Value of sensible heat needed to increase the temperature of acetone in liquid form from 25 to 56 degree Celsius is 4.06 kJ / mol. Value of sensible heat needed to increase the temperature of acetone in vapor form from 56 to 100 degree Celsius is 3.82 kJ / mol. Unit of H is kJ / s.
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