Mixing Problem 2.3

Qo aIt wig i

1000 Liters Amount of salt

Tankoftbrinerdrauineym

t 0at t o min

Q Ct

a Write down an IVP for QA

TQ Qo gramsdd rate in rate out

rate in 1009 r litme.tn loorgram min

rate out Foto r litme.TL QoHoor gram

min

ddtQ 1oor Qooro

b Discuss the solution to the above IVP

Separable exercise to solve

Qlt 105 t Q 105 e0

Q As t 70 Qft 7105 grams

iosQlt 105 g is an equilibrium Soh

µa owner

ETEt

Qft 105 more rapidly as

r increases

c Let gets the amount of salt in the tank in kgWrite down an IVP for qtt

GH kg Q H gram

when q I Q 1000

Q 1000 of

dd too r pooro

dllodfoGL poor 400001I 000

1000doff loor qr

dqt.o.ir 9roo.kmInqloQo9ramTooEokgfam ffoo kg

1963 971d Write down an IVP for the concentration of salt

CHI Lin gramhiler in the tank

Lt gramTiter Qtt grams in 1000 liters

Clt Q H gramsTooo Tiers

Q 1000 C

dd too r ffor

odltffdioor 490IRgram Iiterddf o.lr fooo min

cloj 0ograml.TT

e Write down an IVP for the concentration of salt

MHI in kghiler in the tank

MH KI CH grainsliter liter

when µ 1 C 1000

C 1000 U

doIt 0 I r CRI000d 1000MTt o I r 4000

I 000

1000 dmIt 0 I r ler

Kghiterdat 8 Toot min1

Mo I 000

µlo Q KIliter

f Write down an IVP for the concentration CH in Shiter

but with time S measured in hours

S h r t min

h 6

when 5 1 t Go

t bos s To

ddIsddf ddt o I r 0

dats Go o I r

s 6r I granting

CCoQogramTt.TT

Timedependentmixigprobem

sa

nDQo aH wig i

1000 Liters Amount of salt

TankoftbrineDIE.it

ymt 0

at t 0 minQtt

ddot rate in rate out

rate in009 mr

2 timer 200 gramlmin

rate out Qot fl lmn I 9ramlmin

until the tank fills updd 200 io t