ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.15 : Based on Time Discounting of Money, let y = x / (1 + r) ^ n, where ^ = power, r = interest rate for the period in decimal value, n = number of periods, y = current value, x = future value. According to Present Value Addition Rule, the present value of a set of future payments is equal to sum for present value of each of the payments. In an engineering business, 3 future payments are to be made : $100 after 1 year; $500 after 2 years; $200 after 3 years. (a) Form an equation of y as a function of r. (b) Find the value of y in 5 decimal places if r = 8 %.
ACCOUNTING AND FINANCIAL ENGINEERING - ANSWER 34.15 : (a) First future payment : n = 1, x = $100. Second future payment : n = 2, x = $500. Third future payment : n = 3, x = $200. Then total y = sum of x / (1 + r) ^ n = 100 / (1 + r) + 500 / (1 + r) ^ 2 + 200 / (1 + r) ^ 3. (b) When r = 8 % = 0.08, y = 100 / (1 + 0.08) + 500 / (1 + 0.08) ^ 2 + 200 / (1 + 0.08) ^ 3 = 680.02845 (5 decimal places). 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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Question 41 - According to Raoult's law, the pressure when vapor is completely condensed, P = x(1) P(1) + x(2) P(2) ... + x(n) P(n) when x(1), x(2) ... x(n) are the mole fractions of component 1, 2 ... n and P(1), P(2) ... P(n) are the vapor pressures of component 1, 2 ... n. A vapor at 74 degree Celsius containing 70 mole % water and 30 mole % ethanol is to be completely condensed. At the temperature of 74 degree Celsius vapor pressure is 0.38 atm for water and 0.97 atm for ethanol. What is the minimum pressure the compressor must be operated?
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Question 103 - (a) Let | - > = 1 | x > + 0 | y >, | | > = 0 | x > + 1 | y >. Find the value of 2 | x > + 3 | y > in term of | - > and | | >. (b) Let m to be the reduced mass. Find the value of m in term of Ma and Mb where 1 / m = 1 / Ma + 1 / Mb.
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ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.23 : An engineering company would like to produce 10000 units of control instruments. Let selling price per unit = $10, variable cost per unit = $2, overall fixed cost = $30000. (a) Calculate the income obtained when all units are sold out successfully. (b) Find the overall cost of production. (c) Calculate the percentage of gross profit obtained based on the answers in (a) and (b). (d) Find the minimum units that need to be sold out successfully in order to prevent losses. (e) How many minimum units of instruments that need to be produced in order to prevent losses, if all units produced are sold out successfully?
ENGINEERING DRAWING - EXAMPLE 18.3 : Autocad computer program is used to draw a pipe that is used to transport natural gases for processing. Actual length of the pipe is 10 metres. The pipe has cross sectional area of circle in shape with measured circumference of s = 3 metres. (a) If 10 units are used to represent the actual length of the pipe in computerised engineering drawing, find the diameter of the pipe, d that will be shown in the engineering drawing. (b) If one unit in the program equals to 1 centimetre, find the scale used in the computer program.
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PETROLEUM ENGINEERING - QUESTION 25.1 : Fact 1 : Dry air contains 20.95 % oxygen, 78.09 % nitrogen, 0.93 % argon, 0.039 % carbon dioxide, and small amounts of other gases by volume. Fact 2 : Volume occupied is directly proportional to the number of moles for ideal gases at constant temperature and pressure. Fact 3 : 12.5 moles of pure oxygen is required to completely burn 1 mole of pure octane. Fact 4 : Air-fuel ratio (AFR) is the mass ratio of dry air to fuel present in a combustion process such as in an internal combustion engine or industrial furnace. Fact 5 : Molecular weight of oxygen gas is 31.998 g / mole and molecular weight of nitrogen gas is 28.014 g / mole. (a) Find the molar ratio of nitrogen and oxygen, or (moles of nitrogen) / (moles of oxygen) in dry air, by assuming ideal features of nitrogen and oxygen gases. (b) How many moles of nitrogen are available if dry air is used to completely burn the 1 mole pure octane? (c) Find the mass of fuel of 1 mole of octane with molecular weight of 114.232 g / mole. (d) Find the mass of dry air with 12.5 moles of pure oxygen by assuming only oxygen and nitrogen gases exist in the air. (e) Find the air-fuel ratio (AFR) when octane is used as fuel. (f) Find the fuel-air ratio (FAR) when octane is used as fuel.
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