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)
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Learning outcomes
At the end of this class, you should be able to
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Americanengineering system
cgs units
SI units
Convert between various units
With special emphasis on
molar amount
pressure
temperature
the ideal gas law
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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!
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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)
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Example: Convert 30 m3 /h
into cfm
1.
2.
3.
4.
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Key steps in unit conversion
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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
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‘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
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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
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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?
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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
_______
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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?
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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
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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
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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
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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
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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
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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
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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