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Lecture 1 & 2

by: Lauren Notetaker

Lecture 1 & 2 BEE 2600

Lauren Notetaker
Principles of Biological Engineering
Wu, M

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About this Document

Why model engineered systems? Conservation of Mass Processes governing conservation of mass Common abbreviations Conservation of mass examples
Principles of Biological Engineering
Wu, M
Class Notes
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This 10 page Class Notes was uploaded by Lauren Notetaker on Monday September 21, 2015. The Class Notes belongs to BEE 2600 at Cornell University taught by Wu, M in Summer 2015. Since its upload, it has received 89 views. For similar materials see Principles of Biological Engineering in Behavioral Sciences at Cornell University.

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Date Created: 09/21/15
BEE 2600 Lecture 1 8252015 Slides 5 amp 6 Conservation of mass Example You give a dog 250 mg of an antibiotic What is the concentration of the drug in the dog Mass in dog 50 ma Cone in 350m 50m dog quot 5 L 9L39 Mass in bumquot mot moss 39 dog 3L 6 mm 4 mass 59m mg cumw d 4 0 41 d9 quotimam 4g Derive differential equationsthat describe 39 time dependent changes in drug concentration V Conservation of mass we mtg W Am mantra antibiotic m 4299 g 5quot d9 1st step of deriving a differential equation V 39 Slides 7 amp 8 on o vf ob ww Processes governing conservation of mass De ne control volumequot drug builds up in kidney control volume blood control volume whole dog 1 t 39 Ma erlal transport Dehveva mass om m comm volump and leaves 1 eklmwach o 2 Material stora e g Spud u or on 6 mass 16 Moved Wou 3 Material transformation We radamo n lt56 dug m Common abbreviations De nition of terms m mass g mol of moles mass in grams molecule weight V volume L p density massvolume eg pm0 1 gL c concentration gL ppm parts per million mgkg m mass flow gs or kghr f volume ow US v velocity ms G mass ux gsmz A area m2 Slide 10 1 Example of conservation of mass F 111mg a reactor with water t f t imam am camtam output g m V volume x m Fem fm 250 Lmin fout 5 Lmin 0 How long does it take A 0m At what time t does 3 10 mquot Mass in Mass at ass going Mass going on to ll the reactor reactor time t0 to reactor out of reactor m 2 m6 139 m39m At quot39 hoof At Am mm 2 mm Al MNMN Am 3 39 a At 9390 dm at m WY m 0 3239 quot mum mw Slide 11 amp 12 1 Example of conservation of mass m pw V lm PW fin Inout pw fout Substitute all of the above into the differential equation dm 2 4 Mullen 39 MW 4 V I unih V I W 10 39lt to loom dV At 09K dCA X 39 3931 an ch39 Six Evianq dt 39 A quot 0245mm1o 245cmmr l 1 Example of conservation of mass How long does it take to fill the tank x t 3 dx 025 jo dt 0 x 0246t x t z 0215 lawn Xio t Homio BEE 2600 Lecture 2 8272015 Slides 15 amp 16 Slides 17 amp 18 2 Example of conservation of Slides 19 amp 20 3 Example of conservation of mass In order to grow anything in the reactor nutrients need to be added For example you are preparing a tank of nutrient solution for a hydroponic growth chamber of plants Thus add Nitrogen to reactor eg nitrate ammonia urea h A GM 2Lmm fin fout V immg x 10 Q teenyL 6 virtan 4100 Q F0 Azw m2 N N03 mm39kohk 1 What is the concentration c after 1000 minutes 2 How long does it take for the concentration in the tank to reach 1 of cm Thus this time we are interested in modeling the mass of nutrients 3 Example of conservation of mass Thus this time we are interested in modeling the mass of nutrients Change of mass 0 ass going Mass going nitrate in reactor 39nto reactor out of reactor 391 A 7321 mm quotquot milow At m clm hm ccms taor 39 6min 1 mmm mmm in QN QH m QNV six meowquot m 0 ECf lc 1 Q v QM39QGU V39 Slides 21 amp 22 Example of conservation of mass Slides 23 amp 24 3 Example of conservation of mass Part 2 At what time t does equot 001 cin ie 1 of cm N be 2xto39G t cm he o mam Q JX 39ct a an e 2Mcs e QHL H quart 9 t Qnmq tame t 339 5025Ymh 84ha 1 0QWhat Will you suggest if the time to reach steady state needs to be shortened 4 V 06ch u WitTIL 50W lu v 44mm 3 W m macaw Wu 4 30 W 4 Example of conservation of mass Ammonia in a fish tank Problem from 199739 nal V 9quot 0 Wm 4m i6m a 3 v tim W WW g jilf j F muff N W N wank 39 F out cont Use a mass balance to deVelop a rate equation then terms of the given variables to describe the gt H 5 Slides 25 amp 26 4 Example of conservation of mass Change inmas ass going Mass going V 0f ammonia quot to reactor out of reactor 1 in tank Am mmi At mmwr t 9quot A m a at g quot5quot m nu PM


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