PROCESS CONTROL - EXAMPLE 6.2 : A stream with volumetric flow rate Q enters a cylindrical tank and a stream with volumetric flow rate q exits the tank. The fluid has a constant heat capacity and density. There is no temperature change or chemical reaction occurring in the tank. Develop a model for determining the height of the tank, h. Let V is the volume, A is the cross sectional area, r is the density, m is the mass, where V and A are for the tank, r and m are for the fluid. The rate of mass of fluid accumulation, dm / dt = (Q - q) r. Prove the model to be dh / dt = (Q - q) / A.
PROCESS CONTROL - ANSWER 6.2 : Mass of fluid in tank, m = Vr = hAr. Then d (hAr) / dt = (Q - q) r. Ar (dh / dt) = (Q - q) r leads to the answer A (dh / dt) = Q - q. Finally dh / dt = (Q - q) / A. 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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Mention some of the specialized crushing methods?
PROCESS CONTROL - EXAMPLE 6.3 : The differential equation is 3 dy / dt + 2y = 1 with y(0) = 1. (a) The Laplace transformation, L for given terms are : L (dy / dt) = sY(s) - y(0), L(y) = Y(s), L(1) = 1 / s. Use such transformation to find Y(s). (b) The initial value theorem states that : When t approaches 0 for a function of y(t), it is equal to a function of sY(s) when s approaches infinity. Use the initial value theorem as a check to the answer found in part (a).
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QUANTUM CHEMISTRY AND CHEMICAL ENGINEERING - EXAMPLE 31.1 : As an approximation, let v = Zc / 137 where v is the radial velocity for 1 s electron of an element, c is the speed of light, Z is the atomic number. For gold with Z = 79, find the radial velocity of its 1 s electron, in term of c and percentage of the speed of light. (b) As an approximation, let A x A = 1 - Z x Z / 18769 where A is the ratio of the relativistic and non-relativistic Bohr radius. Find the value of A.
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ENGINEERING DRAWING - EXAMPLE 18.1 : For a Vernier scale of representative fraction (RF) = 1 / 25, calculate the length of the scale for the reading up to 4 metres.
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