applications to first order de

23
Langat Lake

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Slide by MOHD HANIFF BIN OSMAN. Lecturer from Universiti Kebangsaan Malaysia.

TRANSCRIPT

Page 1: Applications to First Order DE

Langat Lake

Page 2: Applications to First Order DE

L angatLake

Aim / Concern:

Page 3: Applications to First Order DE

L angatLake

Aim / Concern:

Page 4: Applications to First Order DE

Aim / Concern:

Prediction model:

...)( tWW

Wdenotes amount of water (ft3) in the lake.

Page 5: Applications to First Order DE

Aim / Concern:

Prediction model:

Differential equation

...)( tW

...dt

dW

Page 6: Applications to First Order DE

Machine input output

Compartmental diagram

Langat Lake Input/inflows

The compartment

outrateinratedt

dW

System

inrate outrate output/outflows

* Amount left = rate in – rate out

Page 7: Applications to First Order DE

Compartmental diagram

Langat Lake Input/inflows

outrateinratedt

dW

inrate outrate output/outflows

Page 8: Applications to First Order DE

Machine input output

Compartmental diagram

Langat Lake

?LFdt

dW

System

inrate outrate h 3ftF ? L

Page 9: Applications to First Order DE

Fill in the blank, please.

Page 10: Applications to First Order DE

?)0( tW

Initial value

Page 11: Applications to First Order DE
Page 12: Applications to First Order DE
Page 13: Applications to First Order DE
Page 14: Applications to First Order DE
Page 15: Applications to First Order DE
Page 16: Applications to First Order DE
Page 17: Applications to First Order DE

Aim / Concern:

Prediction model:

...)( tAA

Adenotes amount of salt (gram) in the tank at time t.

Page 18: Applications to First Order DE

out' rate'in' rate' dt

dA

Page 19: Applications to First Order DE

in' rate'

Page 20: Applications to First Order DE

out' rate'

Page 21: Applications to First Order DE

out' rate'

trateoutflowrateinflowV

tA

tV

tAtc

o )(

)(

Page 22: Applications to First Order DE

out' rate'

044 V

A

tV

tAtc

o

Page 23: Applications to First Order DE

30)0(,200

4 AA

dt

dA