Answer as soon as possible thank you ! CONSERVATION PRINCIPLES A packed column s
ID: 1022648 • Letter: A
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Answer as soon as possible thank you !
CONSERVATION PRINCIPLES
A packed column separator is a cylinder made of stainless steel is 24 feet long and has an outer diameter of 6 inches with a reactor wall thickness of 0.80 inches. It will be filled from end to end with iron catalyst where each catalyst pellet is considered spherical in shape and has a diameter of 0.50 inches. Determine the following: a) What is the inner diameter of the reactor in feet? Determine the exact value then report the answer with two significant digits. b) Calculate the volume of the reactor in cubic feet that will be filled with catalyst. Determine the exact value then report the answer with two significant digits. c) Porosity is the fraction of open space per unit volume filled with catalyst. If this catalyst has a porosity of 0.40, how many pellets will be able to fill the reactor? Determine the exact value then report the answer to the nearest whole number of pellets. d) The catalyst has a unit cost of 150.00 dollars per unit. A unit equals 100 pellets. How much will the amount of catalyst that you determined in PART C will cost in dollars? Report the cost to the nearest whole unit.Explanation / Answer
(a): Given the outer diameter of the cylinder, Ro = 6 inches
Thickness of the cylinder, d = 0.80 inches
Hence inner radious of the cylinder, Ri = ( 6 - 0.80 ) inches = 5.20 inches = 5.20 inches x (1 feet / 12 inches) = 0.43 feet (answer)
(b): Volume of the reactor that will be filled with iron catalyst is equal to the volume of the inner cylinder.
Given, length of cylinder, l = 24 feet,
Inner radius Ri = 0.43 feet
Hence volume = Pi x (Ri)2 x l = 3.14 x (0.43 feet)2 x 24 feet = 14 cubic feet (answer)
(c): Given the porosity = 0.40
Hence fraction of space filled with catalyst = 1 - 0.40 = 0.60
Hence volume of space filled with catalyst = 14 cubic feet x 0.60 = 8.4 cubic feet
Given the diameter of the spherical shaped iron catalyst = 0.50 inches
=> radius of spherical shaped iron catalyst, r = 0.50 inches / 2 = 0.25 inches = 0.02083 feet
Hence volume of a single spherical shaped iron catalyst = (4/3) x Pi x r3 = (4/3) x 3.14 x (0.02083 feet)3
= 3.784x10-5 cubic feet
Hence number of single spherical shaped iron catalyst required = 8.4 cubic feet / 3.784x10-5 cubic feet
= 2.22x105 pallets (answer)
(d): [2.22x105 pallets / 100] x 150 = 3.3x105
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