03 Units and Conversion Students

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Unit Conversions

1st Semester, 2015/16 Session

Dr. Yeoh Hak Koon

DEPARTMENT OF CHEMICAL ENGINEERING

UNIVERSITY OF MALAYA

(KKEK 1123 Chemical Process Principles 1)



Learning outcomes

At the end of this class, you should be able to

D r . Y e o h H a k K o o n 2 0 1 5 2

Americanengineering system

cgs units

SI units

Convert between various units

With special emphasis on

molar amount

pressure

temperature

the ideal gas law



Example:

A correlation between theheight and the mass of people:

where

M = mass in kg h = height in m

What are the units for thecoefficients in the correlation?

Every term must have theunits of _______

Units for the 1st coefficient:

Attempt the remaining terms

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Revision: dimensional consistency

5.2h4.5h4.23M 2

Only terms with the same

units

can be added or subtracted



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Important

Guten Tag

Mingalaba!



Quantity SI Others

Length 2.54 cm0.3048 m

1” 1 ft (or 1’) = 12”

Mass 1 kg 2.205 lbm

Temperature 1oC ch nge

1K ch nge

1.8oF ch nge

1.8oR ch nge

Force 4.45 N 1 lbf 32.174 lbmft/s2

Pressure 101 325 Pa 1 atm = 760 mmHg 14.7 psi

= 1.01325 bar

Energy 4.1868 J

1 kJ

1 cal

0.9478 Btu

Power 0.746 kW 1 hp

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Unit conversion factors to memorize!

these are the‘vocabularies’

History:

lb and pound are

from Latin

“libra pondo”

(a pound of weight)



Example: Convert 30 m3 /h

into cfm

1.

2.

3.

4.

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Key steps in unit conversion



Your turn!

Express 0.996 metric ton/m3 as lbm/ft3

What is the acceleration of gravity in ft/s2?

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Example:

The concentration ofmethanol in a reactor varies with time as follows:

where c is in molarity

t is in minutes

The client requires c to be in

kg/L and t in hours. Do thenecessary.

Solution:

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Changing units of equations

t063.0exp5.4c



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Molar amount of material Concentration Pressure Temperature

Very

important!

Molar amount of material Pressure Temperature Quantities from the ideal gas law



‘Mole’ is actually ‘gmole’, e.g.

12 g C = 1 gmole C = 1 mole C

If we raise it by 1000 times,

12 kg C = 1 kgmole C = 1 kmole C

If we use other units, wedefine similarly

12 tonne C = 1 tmole of C

12 lbm C = 1 lbmole C

12 ounce C = 1 ounce mole C

This allows molecular weights

be expressed in other units whereconvenient, e.g.

For CH4:

What is the mass of 100. lbmole of

HCN in kg?

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1. Molar amount

lbmole

lb16

kmole

kg16

mole

g16 m

or any other

fanciful units



How to derive the key unit

conversion factors (whenyou forget!):

Height of water vs pressure?

1 atmosphere equals to …

1 atm = ? psi (lbf /in2)

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2. Pressure units and scales



Human psychology:

“0” “no pressure” (pump not running)

We are rarely aware of

atmospheric pressure

To reduce mistakes, …

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Pressure scales

http://www.suggestkeyword.com/Y2VudHJpZnVnYWwgcHVtcA/

accessed 07 Sep 2015

How does the operator know

if this pump is running?



Pressure gauges (meters) that

show zero reading at atmosphericpressure give the “gauge pressure”:

Pgauge = Pabsolute – Patm

More human psychology …

Which one is easier to imagineand to read?

101.325 kPa

14.7 psia or “pounds”

34 ft H2O 1 atmosphere or “1 a t m”

1 bar

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continued …

-10

0 barg

Atmospheric Not exact, but

is easy to use and makes little difference at low pressures

“g” or

_______



Examples

What is 250 psi in bars?

The vacuum pressure is defined as P vac

= Patm

– P. Relate it with

gauge pressure Pg.

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Does it matter

if its is gaugeor absolute?



Remember these scales: These require

Derive this:

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3. Temperature units and scales

oC

100

0

oF

212

32

0

K

273.15

273.15

+100

oR

459.67

459.67

+212

32CT8.1FT oo

67.459FTRT

15.273CTKToo

o

1 K 1 oC 1 oF 1 oR

The Fahrenheit gap

is smaller



For temperature changes:

1 K = 1oC 1oR = 1oF 1oC = 1.8oF

Example: convert the units

of the specific heat capacity of water to kcal/kg.oF :

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Converting T

Other than temperature itself,

virtually all other quantitiesthat involve units of

temperature imply T.

K.kg

kJ2.4



Rearranging to give the

universal gas constant:

At STP, one mole of an

ideal gas occupies about22.4L, what is a possiblevalue of R?

e.g.

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4. The ideal gas law

nT

PVR

It can have many

possible units

At least remember one value, e.g.

8.314 kJ/kmol.K



From PV = nRT, at

constant P and T, we have

where

To convert into mass flow rates?

Often volumetric flow rates are

reported at standard conditions,e.g. at 1 atm, 0oC

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Gas flow rates

RTnVP

dt

dnn ,

dt

dVV

This allows interconversion

between volumetric and molar

flow rates of gases

o

oo

P

RTnV

Since we know R, T

o

and P

o

, it gives us

__________________

Commonly seen abbreviations: SCMH, SCFM



For an ideal gas, how do

you convert its volumetricflow rate (at T and P) to thatat standard conditions (at To and Po)?

Solution:

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Example

You must be comfortable moving in

between these two volumetric flow rates



For an ideal gases at a given

P and T:

The mole fractions of

species-k is then given by

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Gas composition: mol/mol = vol/vol

RT

PVn

k

k

P, T

n

1

, n

2

, n

3

…

Moles of

species k

Volume

occupied by

species k

r

r

k

r

r

k

r

r

k

k

V

V

V

RT

P

RT

PV

n

nx

= volume fraction



Summary

The 3 key steps to convert units correctly are:

write units as numerator and denominator

multiply by suitable powers of the conversion factors

simplify the numbers

The common quantities that require extra care with units are:molar amount

pressure: gauge or absolute

temperature, temperature difference

those involving the ideal gas law, e.g. flow rates, volume fractions

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2

2 2

2

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03 Units and Conversion Students