Question 79 - (a) The American Petroleum Institute gravity, or API gravity, is a measure of how heavy or light a petroleum liquid is compared to water. Let SG = specific gravity of petroleum liquid, and V = barrels of crude oil per metric ton. Given the formula for API gravity = 141.5 / SG - 131.5 and V = (API gravity + 131.5) / (141.5 x 0.159), find the relationship of SG as a function of V. (b) An oil barrel is about 159 litres. If a cylinder with diameter d = 50 cm and height h = 50 cm is used to contain the oil, find the volume V of the cylinder in the unit of oil barrel by using the formula V = 3.142 x d x h x d / 4. (c) First reference : 1 cubic metre = 6.2898 oil barrels. Second reference : 1 cubic metre = 6.37 oil barrels. What are the 2 factors that cause the difference in such reference data?
Answer 79 - (a) Substitute API gravity = 141.5 / SG - 131.5 into V = (API gravity + 131.5) / (141.5 x 0.159) will produce V = (141.5 / SG - 131.5 + 131.5) / (141.5 x 0.159) = 1 / (0.159 SG). Then SG = 1 / (0.159 V). (b) Let V = 3.142 x d x h x d / 4 = 3.142 x 50 x 50 x 50 / 4 = 98187.5 cubic centimetres = 98.1875 litres = 98.1875 litres x (1 oil barrel / 159 litres) = 0.6175 oil barrel approximately. (c) Oil density and temperature. 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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CHEMICAL MATERIAL BALANCE - EXAMPLE 2.1 : Two methanol-water mixtures are contained in separate tanks. The first mixture contains 40.0 wt % methanol and the second contains 70.0 wt % methanol. If 200 kg of the first mixture is combined with 150 kg of the second, what are the mass and composition of the product? The symbol of weight percent is wt %.
In engineering economy, the future value of first year is FV = PV (1 i). For second year it is FV = PV (1 i) (1 i). For third year it is FV = PV (1 i) (1 i)(1 i) where FV = future value, PV = present value, i = interest rate per period, n = the number of compounding periods. By induction, what is the future value of $1000 for 5 years at the interest rate of 6%?
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Question 78 - 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.
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?
ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.9 : In the modelling of the total of n rolls of a dice by an engineering student, let D be the random outcome of rolling a dice once. (a) Find the probability of outcome of D = 1, 2, 3, 4, 5 and 6. (b) Find the average score of each rolling of a dice D. (c) Find the expected value, Sn of n rolls of a dice in term of n and D. A new dice has a value of D* = D - 3.5. (d) Find the values of D* for each volume of D = 1, 2, 3, 4, 5 and 6. (e) Find the equivalent model of Sn in term of n and D. (f) Find the expected value of D*.
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