Generating random numbers
Common usage: to get a random number from 1 to N
int n = rand.nextInt(20) + 1;
/ 1-20 inclusive
To get a number in arbitrary range [min, max] inclusive:
name.nextInt(size o
9/8/2017
Pressure
Pressure is defined as the amount of force exerted on a unit area of
a substance:
P=
force N
=
= Pa
area m 2
P=
force lb f
= 2
area
ft
In these pipes the pressure is calculated from
9/8/2017
Open-end Manometer
Measures Gauge Pressure
One surface at Patm
Sealed-end Manometer
Measures Absolute Pressure
Vacuum at sealed end
ChE 317
Pressure Head
P1 P2 = f gh
If we think about this,
9/8/2017
Common Units for Pressure
Unit
1 pascal (Pa)
Definition or
Relationship
1 kg m-1 s-2
1 bar
1 x 105 Pa
1 atmosphere (atm)
101,325 Pa
1 torr
1 / 760 atm
760 mm Hg
1 atm
14.696 pounds per sq.
in
9/19/2017
Equations that Count
Material Balances
For a nonreactive process no more than nMS independent material
balances may be written. nMS is the number of molecular species
involved in the process
9/19/2017
Degree of Freedom Analysis
x + y = 10
x y =0
xy = 3
2 unknowns
3 independent equation
-1 DOF
Overdetermined
Not a set of linear
equations. So even if
DOF=0, cant use
matrix methods.
ChE 317
9/19/2017
Degree of Freedom Analysis
Lets begin with a few algebraic examples
ChE 317
Degree of Freedom Analysis
x + y = 10
2 unknowns
1 independent equation
1 degree of freedom (DOF)
Underdetermined
9/19/2017
Multi-Unit Process
ChE 317
Multi-Unit Process
Overall
2 unknowns ( ,
2 balances (A and B)
0 DOF
Mixing Point
4 unknowns ( , , ,
2 balances (A and B)
2 DOF
ChE 317
10
9/8/2017
When we have a liquid with a free surface the pressure P at any
depth below the free surface is:
P = g h + Po
Po is the pressure at
the free surface
(Po=Patm)
This pressure when measured is c
Random question
Write a program that simulates rolling of two 6-sided dice
until their combined result comes up as 7.
2 +
3 +
5 +
1 +
4 +
You
4 =
5 =
6 =
1 =
3 =
won
6
8
11
2
7
after 5 tries!
9
9/8/2017
Pressure at Base of Fluid Column
Approach 1
The pressure exerted by the weight of the
fluid on the bottom surface is called the
hydrostatic pressure. It is simply the force
exerted on the bas
9/8/2017
Temperature
The temperature of a substance is a measure of the average kinetic
energy possessed by the molecules or atoms of the substance.
ChE 317
Temperature
Kinetic energy cannot be direct
9/8/2017
We could report temperatures in terms of these physical
properties. For example heat until the temperature at which the
resistivity a copper wire is 1.92x10-6 ohm/cm3.
It is more convenient t
9/8/2017
Measurement of Pressure Differences
Apply the basic equation of static fluids to both legs of
manometer, realizing that Pa=Pb.
Pa = P1 + 1 gd1
Pb = P2 + 2 gd 2 + f gh
The General Manometer Eq
9/8/2017
A force balance in the z direction gives:
F
z
= 0 = PS z PS z + z Szg
Pz + z Pz
= g
z
For an infinitesimal element (z0)
dP
= g
dz
ChE 317
Incompressible fluid
Liquids are incompressible i.e.
9/8/2017
Note that the temperature in Cp refers to a temperature interval
(T) while the T in the expression is a temperature. T and T
conversions are handled differently.
First substitute in the conve
9/8/2017
Temperature Conversions
T (K) = T (C ) + 273.15
T (R) = T (F ) + 459.67
T (R) = T (K ) * 1.8
T (F) = T (C ) * 1.8 + 32
T (C) = (T (F ) 32) / 1.8
ChE 317
Example (continued)
Btu
4
Cp
= 0.4
9/19/2017
Equations that Count
Physical Properties and Laws
Two unknown variables may be related by a physical property. For
instance, a tabulated specific gravity, density or equation of state
(for g
9/19/2017
Degree of Freedom Analysis
x + 2 y + 3z = 10
4 x + 5 y + 6 z = 15
7 x + 8 y + 9 z = 20
3 unknowns
2 independent equations
1 DOF
ChE 317
Degree of Freedom Analysis
DOF = 0
Number of equations
9/19/2017
Multi-Unit Process
Unit 1
2 unknowns ( ,
2 balances (A and B)
0 DOF
Mixing Point (again)
2 unknowns ( ,
2 balances (A and B)
0 DOF
ChE 317
Multi-Unit Process
m 3 = 60.0 kg h
m 1 = 60.0 kg
10/15/2017
Gases
ChE 317
Gases
Gases can be pictured at one level as not interacting, free-floating
individual molecules.
Since there is a lot of free space between molecules, gases are
compressible m
10/15/2017
Example
The volumetric flow rate of a stream of propane at 150C and 70.0atm
is being fed to a furnace at the rate of 29.0 m3/hr. What is the flow rate
in kmol/hr
3
kmol C3H8 PV 70.0 atm 29
10/15/2017
Ideal Gas Mixtures: Partial Properties
Partial Pressure of a component of a gas:
pA = yA P
yA =
pA
P
Pure component volume and volume fraction:
PVA = nA RT Divide v A nA
=
= yA
PV = nRT
V
10/15/2017
Ratio Example
Ten cubic feet of air at 70F and 1.00 atm is heate to 610F and compressed to
2.50 atm. What volume does the gas occupy at the new conditions.
n remains constant in this proces
10/15/2017
Standard Temperature and Pressure
STP
PV
T
=n
Ts
PV
s s
R is missing from this expression. All we need to do is define
the standard values for our given units.
Caution: IUPAC Ps 100kPa (0.9
10/15/2017
Textbook Flowsheets
Our flowsheets for the most part have looked like this:
ChE 317
More Likely Specifications
An orifice meter mounted in a process gas line indicates a flow
rate of 24 ft3
10/15/2017
Look It Up
Perrys Chemical Engineers Handbook
CRC Handbook of Chemistry and Physics
NIST Chemistry WebBook
http:/webbook.nist.gov/chemistry
DIPPR Database
ChE 317
Estimate It
There are far
10/15/2017
Example
Liquid acetone (C3H6O) is fed at a rate of 400 L/min into a heated chamber
where it evaporates into a nitrogen stream which enters at 27C and 475 mm
Hg (gauge). The gas leaving the
10/15/2017
Textbook Flowsheets
Our flowsheets for the most part have looked like this:
ChE 317
More Likely Specifications
An orifice meter mounted in a process gas line indicates a flow
rate of 24 ft3
10/15/2017
Solids and Liquids (Mixtures)
Data for many liquid mixtures and many solids dissolved in
liquids are listed in Perrys Handbook (see graph on next slide
for a couple of examples)
In the abse
10/15/2017
Real Flowsheets
Future flowsheets will more than likely have streams that
look like the following:
Since mass balance calculations are more easily done
with moles, part of the job becomes c
10/15/2017
Ideal Gas Mixtures: Daltons Law
The total pressure (P) of an ideal gas mixture is equal to the sum of the
partial pressures (pjs) of each individual component in the gas mixture at
the same