Engineering

Water at 10C lows from a large reservoir to a smaller one through 5 cm-diameter cast iron piping system, as shown in Fig. Q-3. The loss coefficients of various components are shown in the Figure. The elevation at z is 4m and the flow rate in the pipe is 6 L/s. The density and dynamic viscosity of water at 10 degree C are rho = 999.7 kg/m^2 and mu = 1.307 times 10^-3 kg/m s. The roughness of cast iron pipe is 0.00026 m. (a) Determine the average velocity in the pipe. (b) Determine if the flow in the pipe is laminar or turbulent (c) In circular pipes, for laminar flow the friction factor is given by the following relation f = 64.0/Re, and for turbulent flow it can be approximated by the Haaland equation 1/Squareroot f almostequalto -1.8 log [6.9/Re + (epsilon/D/3.7)^1.11], where f is the friction factor, the log is in base 10, Re is Reynolds number, epsilon is roughness, and D is the diameter of the pipe. Determine the friction factor in the piping system. (d) Determine the elevation z_1

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6.6 Lead melts at 620°F and tin melts at 450°F. They form a eutectic containing 62 percent tin at 360°F. The maximum solid solubility of tin in lead at this temperature is 19 percent; of lead in tin, 3 percent. Assume the solubility of each at room tempera- ture is 1 percent. 1 Draw the equilibrium diagram to scale on a piece of graph paper labeling all points, lines, and areas. 2 Describe the solidification of a 40 percent tin alloy. Sketch its microstructure at room temperature, giving the chemical composition and relative amounts of the phases present. 3 Draw the cooling curve for the above alloy. 4 Repeat 2 and 3 for an alloy containing 90 percent tin. 67 Calcium (melting point 1560°F) and magnesium (melting point 1200°F) form a compound Camg, which contains 45 percent calcium and melts at 1320°F. This compound forms a eutectic with pure magnesium at 960ºF and contains 16 percent calcium. The solubility of the compound in magnesium is about 2 percent at the eutectic temperature and decreases to almost zero at room temperature. Magnesium is not soluble in the compound. A second eutectic is formed between the compound and calcium at 830°F containing 78 percent calcium, and there is no solid solubility between the compound and pure calcium. 1 Draw the equilibrium diagram to scale on a piece of graph paper labeling all points, lines, and areas. 2 Describe the slow cooling of an alloy containing 30 percent calcium. Sketch the microstructures at room temperature and give the relative amounts of the phases present 3 Draw the cooling curve. 4 Write the specific equation of the reaction that takes place at each eutectic temperature.

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3. (35 points) Consider a gas-phase reaction that occurs via the following sequence of elementary steps (l; are reactive intermediates): ki = 15-7 A-321 B+1, ** 12 212 ** C +13 213.D k2 = 12 dm² mol st kz = 30 dm’ mot’s k4 = 90 dm mot’ 57 (a) Setting up the problem: (i) Write the stoichiometric numbers (G) for each elementary step, if I molecule of D is formed in each reaction event (e.g., in the overall stoichiometric reaction). (ii) Write out the overall stoichiometric reaction. (iii) Write expressions for the overall reaction rate, r, in terms of the rates of each elementary step, ri. (iv)Write expressions for the overall reaction rate, r, in terms of the rates of formation of each species, r;. (b) Derive the rate expression for the rate of production of D, rd, in terms of rate constants and concentrations of reactants and products by applying the pseudo steady-state hypothesis (PSSH) for all reactive intermediates. (c) Based on the rate law determined in part (b), determine the steady-state effluent concentration of A. C. for a CSTR (10 dm) with inlet volumetric flowrate 50 dm min and inlet concentrations CA=50 mol dm3 and CBo=150 mol dm. (Hint: this is a gas-phase reaction. Is the overall stoichiometric reaction equimolar, and if not, what is the value of £?)

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3. The head-vs-flow rate and efficiency-vs.-flow rate curves for a centrifugal pump pumping water are shown below: 40 35 60 15 Floe rate [eu ft min] The horse-power (HP) required by this pump at a flow rate of 700 ft min is most nearly B. 26 C. 29 D. 31 4. system pumping water. The brake horse-power (HP) required to run this pump under the condition shown is most nearly The figure below shows the pump curve, the system curve, and the efficiency curve for a 45 40 35 30 25 20 15 10 1000 100 200 300 400 500 600 700 800 900 Flow rate [eu ft min] A. 35 B. 40 C. 55 D. 65

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