BIOPROCESS ENGINEERING - EXAMPLE 14.1 : In differential centrifugation of cells with diameter D in centimeter, the square of D is given by D x D = [18n ln (RF / RI) ] / [ (RP - RFF) Wt ] where n is the fluid viscosity (poise), RF is the final radius of rotation (cm), RI is the initial radius of rotation (cm), RP is cell density (g / ml), RFF is the fluid density (g/ml), W the square for the rotational velocity in (radians / s) (radians / s), t is the time required to sediment from RI to RF (s). Derive an equation for W as a function for D, n, RF, RI, RP, RFF and t, with the stated units above, in radian & degree.
BIOPROCESS ENGINEERING - ANSWER 14.1 : By algebraic formula, W = [18n ln (RF / RI) ] / [ (D x D) (RP - RFF) t ] where W is in (radians / s) (radians / s). One radian is approximately 57.288 degrees, then the W (radian) = (57.288) (57.288) W (degree) or W (in radian) = 3281.96 W (in degree). 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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ENGINEERING ECONOMY - EXAMPLE 7.1 : In engineering economy, the future value of first year is FV = PV (1 + i). For second year it is FV = PV (1 + i) (1 + i). For third year it is FV = PV (1 + i) (1 + i)(1 + i) where FV = future value, PV = present value, i = interest rate per period, n = the number of compounding periods. By induction, what is the future value of $1000 for 5 years at the interest rate of 6 %?
Question 79 - (a) The American Petroleum Institute gravity, or API gravity, is a measure of how heavy or light a petroleum liquid is compared to water. Let SG = specific gravity of petroleum liquid, and V = barrels of crude oil per metric ton. Given the formula for API gravity = 141.5 / SG - 131.5 and V = (API gravity + 131.5) / (141.5 x 0.159), find the relationship of SG as a function of V. (b) An oil barrel is about 159 litres. If a cylinder with diameter d = 50 cm and height h = 50 cm is used to contain the oil, find the volume V of the cylinder in the unit of oil barrel by using the formula V = 3.142 x d x h x d / 4. (c) First reference : 1 cubic metre = 6.2898 oil barrels. Second reference : 1 cubic metre = 6.37 oil barrels. What are the 2 factors that cause the difference in such reference data?
ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.29 : An engineering company that produces small biochemical tools applies Installment Sales Method in its accounting. Let A = Installment Sales, B = Cost of Installment Sales, C = Gross Profit, D = Gross Profit Ratio. In year 20X8, let A = $400, B = $250, C = $150. In year 20X9, let A = $450, B = $315, C = $135. If the value of D = 37.5 % in year 20X8 : (a) find the value of D for year 20X9; (b) calculate the realized gross profit = ED / 100, for year 20X8 when the cash collected from sales is E = $100.
The water is superheated steam at 440 degree Celsius and 17.32 megapascals. Estimate the enthalpy of the steam above. From the steam table for water at 440 degree Celsius, enthalpy of steam, h at 18 megapascals is 3103.7 kilojoules per kilogram and at 16 megapascal is 3062.8 kilojoules per kilogram. Assume that h = mP c where P is pressure; m and c are constants at fixed temperature with small differences in P.
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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FOOD ENGINEERING - QUESTION 23.3 : (a) In the measurement of the browning (optical density) of fruit juice at 10 day interval, the following pairs of data are obtained with time t in days and browning or optical density (OD) : t = 0, OD = 0.05; t = 10, OD = 0.071; t = 20, OD = 0.089; t = 30, OD = 0.11; t = 40, OD = 0.128; t = 50, OD = 0.149; t = 60, OD = 0.17. (i) By using Excel or other programs, determine if such browning reaction can be characterised by pseudo zero order kinetics, with strong correlations between the data pairs of t and OD. (ii) When OD = 0.24, the shelf life T of such juice is expired. Calculate the value of T. (b) Let food cost percentage = ( food cost / food sales ) x 100. If total food cost of bread and butter are $25, food cost percentage of bread is 50 % and for butter is 50 %, find the total food sales of bread and butter.
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.
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