ENGINEERING MATHEMATICS - EXAMPLE 8.2 : In the US (United States), one barrel is equal to 42 US gallons and equivalent to 0.15898 cubic metres. One British barrel is equal to 36 Imperial gallons and equivalent to 0.163659 cubic metres. If an oil refinery in England sells 42 Imperial gallons of crude oil to a company in US, how much US gallons of crude oils has been sold?
ENGINEERING MATHEMATICS - ANSWER 8.2 : Volume of crude oil sold in US = 42 x 42 (US gallons) / 0.15898 (cubic metres) x 0.163659 (cubic metres) / 36 (Imperial gallons) = 50.4421 US gallons. 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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A concentric, counter-current heat exchanger is used to cool lubricating oil. Water is used as the coolant. The mass flow rate of oil into the heat exchanger is 0.1 kg / s = FO. For oil, the inlet temperature TIO = 100 degree Celsius and the outlet temperature TOO = 55 degree Celsius. For water, the inlet temperature TIW = 35 degree Celsius and the outlet temperature TOW = 42 degree Celsius. What is the mass flow rate of water in kg / s, FW needed to maintain these operating conditions? Constant for heat capacity of oil is CO = 2131 J /(kg K) and for water is CW = 4178 J /(kg K). Use the equation (FO)(CO)(TIO – TOO) = (FW)(CW)(TOW – TIW).
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BIOPROCESS ENGINEERING - EXAMPLE 14.2 : An aqueous solution with 2.5 g of a protein dissolved in 600 cubic centimeters of a solution at 20 degree Celsius was placed in a container that has a water-permeable membrane. Water permeated through the membrane until the h - level of the solution was 0.9 cm above the pure water. (a) Calculate the absolute temperature of the solution, T in Kelvin, where T (Kelvin) = T (degree Celsius) + 273.15. (b) Calculate the osmotic pressure, P of the solution by using the formula P = hrg where h is level of the solution, r is density of water with 1000 kg per cubic meter, g = 9.81 N / kg as gravitational acceleration. (c) Calculate the concentration of the protein solution, C in kg / cubic meter. (d) Calculate the molecular weight of the protein, (MW) = CRT / P where R = 8.314 Pa cubic meter / (mol K) as ideal gas constant.
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?
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