DIFFERENTIAL EQUATIONS - EXAMPLE 20.2 : During the landing process of an airplane, the velocity is constant at v. (a) If the displacement of the plane is x at time t, find the differential equation that relates t, x and v. (b) The plane has 2 parts of wheels - the front and the back, separated by a distance L. The front part of the wheel touches the land first, that allows the straight body of the plane to form an angle T with the horizontal land. If the vertical distance between the back part of the wheel and the horizontal land is y, find the equation of y as a function of L and T. (c) Find the differential equation that relates dy as a function of dt, v and sin T. (d) Find the differential equation that consist of dy as a function of y, L, v and dt. (e) Find the equation of y as a function of v, L, t and C where C is a constant. (f) When t = 0, prove that y = exp C as the initial value of y.
1 2579PROCESS 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?
1 2546ENVIRONMENTAL 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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