Explain what are the assumptions made on conservation equation?
Answer / Sanjev Kumar Gupta
The conservation equations, which include the continuity, momentum, and energy equations, are fundamental in fluid dynamics. These equations assume that the fluid is continuous, compressible or incompressible, ideal (no viscosity), inviscid, steady or unsteady, and non-reacting or reacting. Assumptions regarding these properties of the fluid determine which specific conservation equation should be used to describe a given fluid flow situation.
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ENGINEERING NUMERICAL METHODS - EXAMPLE 19.3 : There are 2 simultaneous equations : (A1) x + (B1) y = D1 and (A2) x + (B2) y = D2. (a) By using Excel program, find the values of x and y when A1 = 80, A2 = 150, B1 = 52, B2 = 100, D1 = 3.5 and D2 = 2.3. (b) Write the expression of Excel in the form of =MMULT(MINVERSE(W:X),Y:Z) in order to get the values of x and y. W, X, Y and Z may be A1, A2, B1, B2, D1 and D2.
Question 39 - Acetone and ethanol are separated using a distillation column with a partial condenser and partial reboiler. An equimolar, sub-cooled liquid feed enters at 100 kmol / hr and condenses 1 mole of vapor for every 6 moles of feed. The separation requires a distillate vapor that is 95 mol % acetone and bottoms liquid that is 5 mol % acetone. The reflux is returned from the condenser to the column as a saturated liquid and the operation is run at (L / V) = 1.4 * (L / V) min. Assume constant overflow conditions. (a) Feed operating line is y = [ q / (q - 1) ] x - z / (q - 1) where z = 0.5 for equimolar liquid mixture of 2 components, q = (L’ - L) / F where L’ = L + F + (F / 6) for condensation of 1 mole of vapor / 6 moles of feed. What is y = f(x)? (b) The rectifying operating line is y = (L / V) x + (D / V) (xd) where (L / V) min goes through the points A (0.95, 0.95) and B (0.53, 0.69), V = L + D. What is y = f(x)? Let xd = 0.95. (L / V) min is the slope of the 2 points A and B.
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In a triple effect evaporator, the heat transfer for an evaporator is calculated as q = UA (TI – TF) where TI is the initial temperature, TF is the final temperature; U and A are constants. Given that heat transfer for the first evaporator : q(1) = UA (TI – TB); second evaporator : q(2) = UA (TB – TC); third evaporator : q(3) = UA (TC – TF) where q(x) is the heat transfer function, TB is the temperature of second inlet and TC is the temperature of third inlet, prove that the overall heat transfer Q = q(1) q(2) q(3) = UA (TI – TF).
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BIOCHEMICAL ENGINEERING INSTRUMENTATION - EXAMPLE 29.5 : The following formula is used as a reference : (analyte signal) / (internal standard signal) = (f-factor) x (concentration of analyte) / (concentration of internal standard). A solution containing 3 mM of analyte and 4 mM of internal standard gave peak signals of 2 and 3 mamps respectively. Another similar solution containing 2 mM of analyte and 1 mM of internal standard gave peak signals of 1 and 4 mamps respectively. Find the average f-factor.
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