ENGINEERING NUMERICAL METHODS - EXAMPLE 19.1 : Solve the simultaneous equation using simple Excel program : r + s - t = 7, 2r - s = 0, 3r + 2t = 15. Explain the use of functions of MINVERSE and MMULT together with the keyboard C (Ctrl) + S (Shift) + E (Enter).
ENGINEERING NUMERICAL METHODS - ANSWER 19.1 : By using Microsoft Excel, r = 3.22, s = 6.44, t = 2.67. MINVERSE, or =minverse is used to inverse the 3 x 3 matrix with constants of r, s, t. MMULT, or =mmult can be used to obtain the answers by functions (inversed matrix of 3 x 3, constants of 7 and 0 and 15). CSE is an Excel function to perform quick calculations for the cells. 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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PROCESS DESIGN - EXAMPLE 21.3 : According to a heuristic of chemical engineering plant design, assume a pressure difference dP = 4 psi for each 10-ft rise in elevation. A pump is needed to pump liquid from a storage tank at a lower elevation to a heating tank at a higher elevation with the elevation difference of 60 ft. (a) Find the pressure loss due to such elevation. (b) If the required minimum inlet pressure to the heating tank is 9 psi, with 1 control valve is installed between pump and heating tank, what is the dP minimum required for the control valve and the entrance to the heating tank when the heuristic mentions that at least 10 psi is required for the control valve? (c) The pressure at the inlet of the pump is 8 psi and the flowrate of the liquid produces pressure head of 50 psi. What is the total pressure produced by the pump? (d) Assume a pipeline dP of 2 psi / 100 ft for liquid flow in a pipe according to heuristic, what is the approximate maximum length of the pipe in ft that can be installed between the pump and the heating tank?
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QUANTUM COMPUTING - EXAMPLE 32.6 : (a) Let H | 0 > = 0.707 ( | 0 > + | 1 > ), H | 1 > = 0.707 ( | 0 > - | 1 > ). Find the values for H | 0 > + H | 1 > and H | 0 > - H | 1 >. (b) In quantum computing, a qubyte is a quantum byte, or 8 quantum bits, a sequence processed as a unit. A qubit is a quantum bit. According to Alexander Holevo in his theorem, n qubits cannot carry more than n classical bits of information. What is the maximum amount of classical bits of information that can be carried by 1 qubyte.
ELECTRICAL TECHNOLOGY - EXAMPLE 16.3 : In the design of a solar power system steps of calculations below are followed : (a) The power output of the inverter of the solar panel is 100 watts. What is the power input, Pin to the inverter when the efficiency of the inverter is 50 %? (b) If the rated power of the inverter is 300 watts, how many inverter is needed for the solar panel? (c) Charge controller of V = 12 volts is used to supply power to the inverter. What is the input current I to the inverter? (d) If the charge controller capacity is 10 A, how many charge controllers are needed? (e) If a biochemical mixer consumes 100 watts, running for 2 hours per day, what is the energy consumption in kilowatt hour per day? (f) What is the input energy needed when the efficiency of the inverter is 50 %? (g) If your area receives 2.88 hours of full sunlight per day, how much energy, in kilowatt hour can be produced per day when one solar panel can produce 20 watts of power? (h) If you know that you have to produce total energy as the answer for (f), how many solar panels are needed? (i) Each V = 12 V battery has 5 ampere hours. If the total energy needed is in answer (f), then how many batteries are needed to run the biochemical mixer if without sunlight for 3 days?
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CHEMICAL MATERIAL BALANCE – EXAMPLE 2.6 : According to Raoult's law for ideal liquid, x (PSAT) = yP where x is mole fraction of component in liquid, y is mole fraction of component in vapor, P is overall pressure and PSAT is saturation pressure. A liquid with 60 mole % component 1 and 40 mole % component 2 is flashed to 1210 kPa. The saturation pressure for component 1 is ln (PSAT) = 15 - 3010 / (T + 250) and for component 2 is ln (PSAT) = 14 - 2700 / (T + 205) where PSAT is in kPa and T is in degree Celsius. By assuming the liquid is ideal, calculate (a) the fraction of the effluent that is liquid; (b) the compositions of the liquid and vapor phases. The outlet T is 150 degree Celsius.
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