PETROLEUM ENGINEERING - QUESTION 25.2 : (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?
PETROLEUM ENGINEERING - ANSWER 25.2 : (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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Question 61 – A biochemical trolley of mass 15 kg is towing a trailer of mass 5 kg along a straight horizontal pathway. The trailer and the trolley are connected by a light inextensible tow-bar. The engine of the trolley exerts a driving force of magnitude 100 N. The trailer and the trolley experience resistances of magnitude 10 N and 30 N respectively. (a) Form 2 equations with unknowns T and a, that represents the equilibrium for the 2 systems of the trolley and trailer. (b) Solve the simultaneous equations from the 2 equations that are obtained in part (a) of this question. T is the tension of the tow-bar and a is the acceleration.
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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.
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HEAT TRANSFER - EXAMPLE 5.3 : In a cylinder with a hollow, let a is outside radius and b is the inside radius. In a steady state temperature distribution with no heat generation, the differential equation is (d / dr) (r dT / dr) = 0 where r is for radius and T is for temperature. (a) Integrate the heat equation above into T(r) in term of r. (b) At r = a, T = c; at r = b, T = d. Find the heat equation of T(r) in term of r, a, b, c, d.
Question 94 - The resolution of separation, Rs for chromatography is given by the formula Rs = (difference in retention time) / (average width at the base). In a chromatogram, 3 peaks a, b and c are found. Average widths W at the bases of the solutes are : Wa = 20 s, Wb = 40 s, Wc = 30 s. Resolutions of separation, Rs for solutes b and c in comparison to a are 2 and 4 respectively. The differences in retention times T for b and c in comparison to a are (Tb - Ta) and (Tc - Ta), Ta = Tc - Tb : (a) Form 2 equations involving Rs as a function of Wa, Wb, Wc, Ta, Tb and Tc. (b) Find the values of Ta, Tb and Tc.
QUANTUM CHEMISTRY AND CHEMICAL ENGINEERING - EXAMPLE 31.9 : When an algebraic product is defined on the space, the Lie bracket is the commutator [x,y] = xy - yx according to Lie algebra in mathematics. If [p,x] f(x) = px f(x) - xp f(x), p = -ih d / dx, find the value of [p,x] in term of i and h.
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