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| M.A.H.Y.
Khoory & Co. Trading
> FAQs
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1.
System |
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1.1
A system most specifically
a fluid (i.e. liquid)
system consists
of a continuous
fluid body and the
devices that contain
it. The system starts
at the inlet(s)
and ends at the
outlet(s) including
the pipes and tanks
(I am referring
to open vs. closed
systems). The system
can generate heat
(i.e. friction)
or loose heat (through
a heat exchanger
for example), it
can also do work
(i.e. pump. inductor,
etc.). It is critical
to clearly identify
the inlet and outlet
points of the system.
In a typical pumping
system where fluid
is pumped from one
tank to another,
the inlet point
is the surface of
the suction tank
and the outlet point
is the surface of
the discharge tank.
Sometimes the discharge
point can be difficult
to identify. An
example is the case
where the fluid
is pumped up to
an elevation, say
z2 , and is then
transferred to a
troth which takes
it down to an elevation
z3.. Which is the
exit point of the
system z2 or z3?
The answer is z2.
When the fluid hits
the troth which
is an open pipe,
no more energy is
required from the
pump to push the
fluid further, gravity
takes over. Let’s
make this a little
trickier, what happens
if the troth is
a pipe, is the discharge
point now z3? Depends.
If the pipe is full
all the way to z3
then yes, if the
pipe is not full,
then no. The discharge
point is the point
where the fluid
fails to completely
fill the pipe.
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1.2
A siphon is a system
of pipe or tubing
with the fluid inlet
- the surface of
the inlet reservoir
- at a higher elevation
than the outlet
and where some portion
of the fluid path
is higher than the
inlet point. The
potential energy
of the fluid at
the inlet of the
siphon is higher
than the potential
energy at the outlet,
this difference
in energy drives
the fluid through
the system. How
high can the siphon
piping go above
the inlet? This
depends on the local
barometric pressure.
If the barometric
pressure or head
is 34 feet of water,
which is the value
at sea level, then
the maximum rise
after the inlet
point is 34 feet
when the fluid is
water.
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1.3
No, not really,
sometimes it might
be handy to run
a pipe from an elevated
tank (starting from
the fluid surface
moving upwards and
then downwards)
to a lower location
without installing
a pump. The system
should work as long
as the line was
full. Of course,
at some time or
other the line will
be emptied and then
the problem would
be how to refill
the line. A higher
tank could be used
to refill the line
but this adds more
complication. The
practical approach
would be to pump
the fluid downwards
to ensure that fluid
could always be
transferred. Or
alternatively, run
a line from directly
underneath the inlet
tank in a path that
brings it continuously
downwards to the
discharge point.
In this case the
piping must be of
sufficient size
to deliver the flow
and head required
at the discharge
point.
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1.4
To start, head is
not equivalent to
pressure. Head is
a term which has
units of a length
or feet. In the
following equation
(Bernouilli’s equation)
each of the terms
is a head term:
elevation head h,
pressure head p/g
and velocity head
v2/2g. Head is equal
to specific energy,
of which the units
are lbf-ft/lbf.
Therefore the elevation
head is actually
the specific potential
energy, the pressure
head, the specific
pressure energy
and the velocity
head is the specific
kinetic energy (specific
means per unit weight).
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So
what is the difference?
Head is energy per
unit mass whereas
pressure is a force
per unit area. |
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1.5
The nozzle manufacturers
will normally give
the Dp (pressure
drop) vs. flow for
their nozzles. Since
the purpose of a
nozzle is to accelerate
the fluid, we might
expect that the
velocity head to
be mentioned. Two
factors need to
be considered when
the fluid goes through
the nozzle:
1.
friction is increased
due to the high
velocity through
the restriction
and
2.
the fluid velocity
is increased which
requires additional
energy (kinetic
energy).
Why
does the higher
velocity require
additional energy?
Well consider
this situation,
if we had a restriction
(such as a valve)
and the fluid
went back up to
its initial velocity,
no additional
energy would be
required other
then the friction
energy. However,
nozzles are usually
positioned at
the discharge
point of the system
which means that
a velocity increase
for the fluid
as it leaves the
system affects
the energy balance
causing the kinetic
energy to increase.
The kinetic energy
increase which
is the velocity
head must be supplied
by the source
of work in the
system, the pump.
The manufacturers
don't really want
to complicate
matters by giving
two pressure losses,
it is simpler
to give the one
pressure loss
required to run
the nozzle at
a given flow rate.
Their philosophy
is, if you supply
the required pressure
ahead of the nozzle,
the nozzle will
produce the required
effect and don't
bug me about the
velocity. In other
words, make sure
that you have
enough pressure
ahead of the nozzle.
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1.6
When designing a
new system, if we
assume a pressure
drop across the
valve of 10 ft of
fluid, then it will
be generally possible
to select a valve
that will give this
pressure drop at
a reasonable opening
of say 90%. In other
words, by using
a Dp of 10 ft for
the pressure drop,
we have fixed one
of the parameters
required to size
a valve, without
unduly restricting
the task. 10 ft
of pressure drop
is a common value
used in designing
systems with control
valves. This criteria
will generally result
in a valve size
one size smaller
than the line (i.e.
if the line is 8",
the valve is 6").
In
the case of existing
systems where
the control valve
is in place, we
should be more
careful. While
the system is
operating, the
position of the
valve should be
noted. The manufacturers
tables for this
valve will give
the pressure drop
corresponding
to the flow rate
and valve opening.
This pressure
drop should be
used in the calculations
for Total Head.
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1.7
After
the initial start
of a pump, the high
point of a system
will have to be
reached before the
system is entirely
filled. When the
system is filled
the high point is
no longer relevant
since the static
head required is
equal to the elevation
of the discharge
point minus the
elevation of the
inlet point. During
the initial phase,
the discharge point’s
elevation is continually
changing as it moves
towards the outlet.
If the high point
of the line is unusually
high, then during
the start-up it
may require more
head than is available.
To avoid this, make
sure that the shut-off
head is greater
than the static
head required to
reach the high point.
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1.8
The pressure
drop associated
with each piece
of equipment is
additive.
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1.9
Fittings
are all the miscellaneous
pipe connections
(tees, elbows, Ys,
etc.) .), sometimes
known as hardware,
required to run
pipes and their
branches in various
directions to their
destination. Manual
valves are also
considered fittings.
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1.10
To drive
fluid through a
piece of equipment
there must be a
force at the inlet
greater than the
force at the outlet.
These forces are
converted to pressure,
which is more convenient
in a fluid system.
The difference (or
drop) in pressure
between the inlet
and outlet is proportional
to the overall force
pushing the liquid
forwards. If we
convert pressure
drop to head then
we obtain the pressure
drop value in terms
of head (i.e. fluid
column height) or
pressure head.
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1.11
If a pump is sized
for a greater flow
and head that is
required for the
present conditions,
then a manual valve
at the outlet of
the pump can be
used to throttle
the flow down to
the present requirements.
Therefore, at a
future date the
flow can be increased
by simply opening
a valve. This however
is wasteful of energy
and a variable speed
drive should be
considered.
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1.12
No,
the N.P.S.H. available
is the head in absolute
fluid column height
minus the vapor
pressure (in terms
of fluid column
height) of the fluid.
Close, but no cigar.
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1.13
No, the Total Head
is the difference
in head between
the discharge and
the suction.
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1.14
The N.P.S.H available
can be calculated
for a specific situation
and depends on the
barometric pressure,
the friction loss
between the system
inlet and the pump
suction flange,
and other factors
(see book). The
N.P.S.H. required
is given by the
pump manufacturer
and depends on the
head, flow and type
of pump. The N.P.S.H.
available must always
be greater than
the N.P.S.H. required
for the pump to
operate properly. |
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1.15
First, calculate
the Total Head of
the system. Then,
using a control
volume, set one
limit at the point
where the pressure
head is required
and the other at
the inlet or outlet
of the system. Apply
an energy balance
and convert all
energy terms to
head. The resulting
equation gives the
pressure head at
the point required
(see book).
other? The most
common reason
for this calculation
is to establish
the pressure ahead
of a control valve
which is required
to size the valve.
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1.16
All systems require
a means of flow
control. The plant's
output requirements
may change causing
flow demand to vary
and therefore the
various systems
throughout the process
must be able to
modify their output
flow rate. To achieve
this, pumps are
sized for the maximum
anticipated flow
rate. The most frequent
means of reducing
the output flow
rate is to have
a line which re-circulates
flow back to the
suction tank. Another
method is to have
a valve in the discharge
line which reduces
the output flow
rate when throttled.
Either method works
well, but there
is a penalty to
be paid in consumption
of extra power for
running a system
which is oversized
for the normal demand
flow rate. A solution
to this power waste
is to use an electronic
variable speed drive.
For a new installation
this alternative
should be considered.
This provides the
same flow control
as a valved system
without energy waste.
other? The most
common reason
for this calculation
is to establish
the pressure ahead
of a control valve
which is required
to size the valve.
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1.17
The head and flow
produced by a pump
is the result of
centrifugal force
imparted to the
liquid by the impeller.
Centrifugal force
is directly proportional
to impeller diameter
and rotational speed.
We can affect the
centrifugal force
by either changing
the impeller diameter,
which is difficult,
or varying the impeller
speed, which of
course is what a
variable speed drive
does. The family
of curves shown
on pump performance
charts corresponds
to the performance
of a pump at constant
speed with various
impeller sizes.
If we keep the impeller
size constant and
vary the speed of
the pump, a similar
set of curves for
different pump speeds
is produced. Therefore,
when a variable
speed drive is used,
only the required
pump head and flow
is produced resulting
in an appropriate
power consumption.
other? The most
common reason
for this calculation
is to establish
the pressure ahead
of a control valve
which is required
to size the valve.
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2.
Pump or Performance
Curve
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2.1
Total Head is the
difference between
the head at the
discharge vs. the
head at the inlet
of the pump. Total
head is a measure
of a pump’s ability
to push fluid through
a system. This parameter
(with the flow)
is a more useful
term than the pump
discharge head since
it is independent
of a specific system.
Also Total Head,
just as any head
at any location
in the system, is
independent of the
fluid density.
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2.2
Fluid layers move
at different speeds
depending on their
position with respect
to the pipe axis.
The velocity is
zero at the pipe
wall and maximum
at the pipe center.
This difference
in velocity between
fluid layers is
a source of friction.
Another source of
friction is the
interaction between
the fluid layers
close to the pipe
wall and the pipe
roughness or the
small peaks and
valleys on the wall
(for turbulent flow
only). The sum of
these two sources
of friction is the
total friction due
to fluid movement.
Friction head is
the energy loss
due to fluid movement
and is proportional
to the flow rate,
pipe diameter and
viscosity. Tables
of values for friction
head are available
in many references.
The Colebrook and
Darcy equations
provide a method
of calculating friction
head for Newtonian
fluids. Another
component of friction
head is the pressure
drop due to fittings.
Many references
supply the data
for determining
the friction loss
due to fittings.
The 2K method is
recommended (see
book).
other? The most
common reason
for this calculation
is to establish
the pressure ahead
of a control valve
which is required
to size the valve.
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2.3
Velocity head is
the kinetic energy
of the fluid particles.
Velocity head difference
is the difference
in kinetic energy
between the inlet
and outlet of the
system.
other? The most
common reason
for this calculation
is to establish
the pressure ahead
of a control valve
which is required
to size the valve.
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2.4
The static head
or total static
head is the potential
energy of the system.
It is the difference
between the elevation
of the outlet vs.
the inlet point
of the system.
other? The most
common reason
for this calculation
is to establish
the pressure ahead
of a control valve
which is required
to size the valve.
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2.5
The Net Positive
Suction Head (N.P.S.H.)
is the head at the
suction flange of
the pump less the
vapour pressure
converted to fluid
column height of
the fluid. The N.P.S.H.
is always positive
since it is expressed
in terms of absolute
fluid column height.
The term "Net"
refers to the actual
head at the pump
suction flange and
not the static head.
The N.P.S.H. is
independent of the
fluid density as
are all head terms.
other? The most
common reason
for this calculation
is to establish
the pressure ahead
of a control valve
which is required
to size the valve.
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2.6
1.
Flow rate through
the pump and everywhere
throughout the system.
2. Physical parameters
of the system: length
and size of pipe,
no. of fittings
and type, elevation
of inlet and outlet.
3.
Equipment in the
system: control
valves, filters.
4.
Fluid properties:
temperature, viscosity
and specific gravity.
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2.8
Start
the pump with a closed
discharge valve. |
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2.9
A
performance curve
is a plot of Total
Head vs. flow rate
for a specific impeller
diameter. The plot
starts at zero flow.
The head at this point
corresponds to the
shut-off head of the
pump, or point A.
The curve then decreases
to a point where the
flow is maximum and
the head minimum,
point B. This point
is sometimes called
the run-out point.
Beyond this, the pump
cannot operate. The
pump's range of operation
is from point A to
B. |
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2.10
A
centrifugal pump consist
of an impeller rotating
within a fixed casing
or volute. Because
the impeller blades
are curved, the fluid
is pushed in a tangential
and radial direction.
A force which acts
in a radial direction
is known as a centrifugal
force. This force
is the same one that
keeps water inside
a bucket which is
rotating at the end
of a string. |
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2.11
The
B.E.P. (best efficiency
point) is the point
of highest efficiency
of the pump. All points
to the right or left
of B.E.P have a lower
efficiency. The impeller
is subject to non-symmetrical
forces when operating
to the right or left
of the B.E.P.. These
forces manifest themselves
as vibration depending
on the speed and construction
of the pump. The most
stable area is near
or at the B.E.P. |
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3.
Calculations
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3.1
Barometric
pressure is the
air pressure in
absolute terms in
the local environment.
The air pressure
is highest at sea
level and gradually
diminishes with
elevation. Barometric
pressure is often
expressed in psia
(pound per square
inch absolute) or
feet of water absolute.
The barometric pressure
at sea level is
14.7 psia or 34
feet of water absolute.
Barometric pressure
is used to calculate
the N.P.S.H. available,
which is required
to determine if
the pump will operate
properly as designed.
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3.2
Your elevation above
sea level varies
with your location.
Your local airport
can give you their
elevation and barometric
pressure. The relationship
between elevation
and barometric pressure
is well documented
and available in
many reference books
as charts or tables.
You can find your
local elevation
on a topographic
map and determine
the barometric pressure
at your location.
For example, the
air pressure at
sea level is 14.7
psia, at 10,000
feet it is 10.2
psia, and at 35,000
feet (the cruising
altitude of most
passenger jets)
3.5 psia. The local
barometric pressure
is required to calculate
the N.P.S.H. available
at the pump suction.
Ever
see a movie where
people and things
are sucked out
of an airplane
after the bad
guy shoots a hole
through a window.
Well at a 35,000
feet altitude,
an object located
over a 12” diameter
hole (approximate
size of a window)
will be subject
to a force of
1270 pounds, frightening
isn’t it?
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3.3
For turbulent flow,
the Colebrook equation
to calculate the
friction factor
followed by the
Darcy equation to
get the friction
head. For laminar
flow, the laminar
flow equation followed
by the Darcy equation.
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3.4
A graphical representation
of the Colebrook
and laminar flow
equation.
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3.5
A technique used
to solve for a non-explicit
variable in an equation.
An example is the
friction factor
in the Colebrook
equation. The technique
can resolve a complex
equation very quickly,
usually converging
to a solution within
4 iterations (see
book).
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3.6
The Reynolds
number is proportional
to the kinematic
viscosity, the average
velocity and the
pipe inside diameter.
The kinematic viscosity
(n) is the ratio
of the absolute
viscosity to the
fluid density.
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The
Reynolds number is
a non-dimensional
number (i.e. has no
units). It combines
3 important characteristics
of the system and
the fluid, velocity,
viscosity and density.
The diameter is termed
the characteristic
length. One of the
many uses for this
number is to establish
if the flow is laminar
or turbulent. A Reynolds
number below 2000
indicates laminar
flow and above 4000
turbulent flow.
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3.7
The Colebrook equation
gives the value
of the friction
parameter f with
respect to the Reynolds
number and the pipe
roughness. When
the Reynolds number
is small, below
2,000 (laminar flow
region), pipe roughness
has no effect at
all. When the Reynolds
number is between
4,000 and 50,000,
that is low velocity
and/or high viscosity,
then the influence
of pipe roughness
is as equally important
as the effect of
velocity. When the
Reynolds number
is large, above
50,000, that is
high velocity and/or
low viscosity, then
the friction is
entirely dependent
on pipe roughness.
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3.8
Any fitting inserted
into a pipe run
has an effect since
it either obstructs
the flow or re-directs
it or both. Most
common fittings
have been studied
and their effect
quantified, the
results are available
in many reference
books.
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3.9
One fluid path from
inlet to a selected
outlet is used for
the calculation
of Total Head. This
path is assumed
to require the highest
Total Head, if there
is a doubt about
the head required
for the other path
then the calculation
is done on the other
path and a comparison
is made. Also the
velocity head input
difference to the
two separate branches
needs to be added
to the Total Head.
This however is
normally a small
and negligible term
(see book for a
detailed explanation).
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3.10
The Colebrook equation
is the most accepted
formula for calculating
the pressure or
head drop due to
friction in pipes
for Newtonian fluids.
This equation relates
the friction factor
to the Reynolds
number and the pipe
roughness. The friction
factor is then used
in the Darcy formula
(see book) to calculate
head drop. For non-Newtonian
fluids, which is
mostly slurries
of one kind or another,
the process is much
more complicated
and many factors
are taken into account.
Some of these factors
are: particle size
and distribution,
settling velocity
of the particles
in the mixture,
viscosity variation
of the mixture,
solids transportation
mode, etc.
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4.
General
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4.1
I haven't found
yet any one comprehensive
source whose theme
matched my interests.
At first, I found
this discouraging,
and then it dawned
on me that this
was a great opportunity.
I was looking for
something not readily
available or published.
Since I was working
in the frozen north
with lots of time
on my hands I wrote
my own book. However,
I did not work entirely
in a vacuum. I consulted
the following books:
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1.
Hydraulic Institute
Engineering Data Book,
Cleveland, Ohio, 1979
2. Goulds Pump Manual,
Seneca Falls, New
York, 1972
3. The Chemical Engineering
Guide to Pumps, Ed.
by K. McNaughton,
McGraw-Hill Publications
Co., New York, 1984
4. Durco Pump Engineering
Manual, The Duriron
Co., 1960
5. Principles of Unit
Operations, A. Foust,
L.A. Wenzel, C.W.
Clump, L. Maus, L.B.
Anderson, John Wiley
& Sons, New York,
1960
6. The Piping Handbook,
edit. Reno C. King,
5th Edition, McGraw
Hill, New York, NY
1973
7. Slurry Transport
Using Centrifugal
Pumps, K.C. Wilson,
G.R. Addie, R. Clift,
Elsevier Science Publishers
Ltd., Crown House,
Linton Road, Barking,
Essex 1G11 8JU, England
8. Cameron Hydraulic
Data, Ed. by C.R.
Westaway & A.W.
Loomis, 16th edition,
Ingersoll-Rand, Woodcliff,
New Jersey, NJ 07675
9. Some Pipe Characteristics
of Engineering Interest,
L.F. Moody, Houille
Blanche, June 1950
10. Turbulent Flow
in Pipes with Particular
Reference to the Transition
Region between the
Smooth and Rough pipe
Laws, C.F. Colebrook,
J. Inst. Civil Engrs.
(London), February
1959
11. Fluid Mechanics
with Engineering Applications,
R.L. Daugherty &
J.B. Franzini, 7th
edition, McGraw-Hill
Book Company, New
York, NY
12. Esso, Product
Information, Lubricants
and Specialties, 1990
13. Van Nostrand Reinhold
Encyclopedia of Chemistry,
ed. D.M. Considine,
4th edition, Van Nostrand
Reinhold Company,
1984, New York
14. Chemical Engineering,
William B. Hooper,
August 24, 1981
15. The Pump Handbook,
McGraw Hill
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4.2
Different liquids
boil at different
temperatures for
a given air pressure.
For example, water
boils at a temperature
of 212 °F at an
air pressure of
14.7 psia (the pressure
at sea level). However,
a temperature of
189 °F is required
to boil water at
a pressure of 11
psia which is the
air pressure at
8,500 feet above
sea level, the altitude
of Mexico city.
Just because water
boils at a lower
temperature in Mexico
city doesn’t mean
that it takes a
shorter time to
boil an egg. The
same amount of heat
transfer is required
to get the egg to
the right consistency
regardless of water
temperature. It
will take longer
to transfer enough
heat to cook the
egg if the water
is boiling at a
lower temperature
than a higher one.
We are so used to
water boiling at
the same temperature
that it is very
surprising to find
that it takes longer
than 4 minutes to
boil a 4 minutes
egg in Mexico city.
How much longer
I don’t know, I’d
have to go to Mexico
city. If there are
any Mexico city
residents out there
on the web, please
try the experiment
and let me know.
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4.3
Pressure is said
to be negative when
it is less than
the local barometric
or atmospheric pressure.
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4.4
A pressure measurement
that is absolute
is not related to
any other. The atmospheric
pressure at sea
level is 14.7 psia
(pounds per square
inch absolute),
that is, 14.7 psi
above zero absolute.
Relative pressure
is always related
to the local atmospheric
pressure. For example,
10 psig (pound per
square inch gauge)
is 10 psi above
the local atmospheric
pressure. Most pressure
measurements are
taken in psig which
is relative to the
local pressure.
Pressure measurements
do not normally
have to be corrected
for altitude since
all the measurements
you might do on
a system are relative
to the same atmospheric
pressure therefore
the effect of elevation
is not a factor.
An important exception
to this is when
taking a pressure
measurement at the
pump suction to
determine the N.P.S.H.
available. This
pressure measurements
is converted to
absolute pressure
which should be
corrected for altitude.
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4.5
A control volume
is a theoretical
boundary which helps
delimit the extent
of a system, particularly
all its inputs and
outputs. The principles
of conservation
of mass and energy
can then be applied
within this region.
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4.6
Because of the principle
of conservation
of energy, any energy
gain or loss in
a system must be
accounted for. Therefore,
making an energy
balance is the process
of identifying all
the sources of energy
gain or loss and
adding them up.
The result must
be equal to zero.
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4.7
The system equation
has on the left
hand side the Total
Head (difference
between the pump
discharge head and
suction head), and
on the right hand
side, all the terms
which impede fluid
flow such as: friction,
velocity, elevation
difference, etc.
An energy balance
is used to derive
the system equation.
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4.8
No, Total
Head is a term that
is used only for
a pump.
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4.9
An inductor
can raise the pressure
of a fluid by using
another fluid at
a higher pressure.
The company Schute
& Koerting manufacture
these devices.
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4.10
Consider
a two pump system
where one of the
pumps is in poor
running condition
as compared to the
other. This could
be due to: worn
or damaged impeller,
worn casing, worn
bearings and shaft,
wrong impeller,
etc. Any or a combinations
of these factors
will have an effect
on the pump's performance.
The efficiency of
the pump will be
affected as well
as the head and
flow. It is difficult
to predict the resulting
performance curve
without doing tests.
However, unless
the pump has gaping
holes, the performance
curve should look
similar to that
of the good pump
but with a lower
capacity and head.
Let's assume that
there is negligible
friction loss between
the discharges of
pumps A or B and
the header, also
the head at the
inlet of both pumps
is the same. The
operating point
is point 1 on curve
A which corresponds
to 500 USGPM and
96 ft. The curve
for the bad pump
B, being slightly
lower will contribute
265 USGPM at 96
ft since it must
operate at the same
head as pump A.
Therefore, the total
flow will be 765
USGPM. If we had
two good pumps the
total flow would
be 1000 USGPM instead
of 765 USGPM. The
head is not affected
since it is the
pump with the higher
head which will
control the pressure
head in the discharge
header by forcing
the other pump to
reduce its flow
to match the higher
pressure head. This
what is meant when
people say that
one pump is fighting
the other. Improperly
designed suction
or discharge piping
can have this effect
also.
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4.11
The best
that the damaged
pump can do is to
produce the head
corresponding to
its shut-off head
DHC (point 2) at
0 flow. Since the
head produced by
the good pump is
higher, there will
be flow through
the damaged pump
in the reverse direction.
The flow however
will be impeded
since the pump can
produce some head.
The system behaves
as a branch system.
The branch flow
sees a head drop
which is the sum
of the shut-as a
branch system. The
branch flow sees
a head drop which
is the sum of the
shut-off head of
the damaged pump,
plus any friction
loss, plus the static
head of the suction
tank on the inlet
of the damaged pump.
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5.
Fluid
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5.1
By definition,
the specific gravity
of a fluid is:
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where
rF is the fluid density
and rW is water density
at standard conditions. |
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5.2
An inductor
can raise the pressure
of a fluid by using
another fluid at
a higher pressure.
The company Schute
& Koerting manufacture
these devices.
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5.3
It is the
relationship between
the tangential stress
or shear within
the fluid (i.e.
the friction force
between layers per
unit surface) and
the velocity gradient
or shear rate (i.e.
the difference in
speed between fluid
layers divided by
the distance between
them) which defines
whether a fluid
is Newtonian or
not. If the relationship
is linear and the
fluid has zero stress
at zero velocity
gradient then it
is Newtonian (see
Table A2) for a
graphic representation
of stress vs. velocity
gradient. Many fluids
do not behave in
the well ordered
fashion of Newtonian
fluids. These are
known as non-Newtonian
fluids. They fall
in several categories
(see Table A2) depending
on what shape the
stress vs. velocity
gradient takes.
For these fluids,
the velocity gradient
is dependent on
the viscosity. That
is, the velocity
affects the viscosity
resulting in a much
higher (or in some
cases lower) stress
than for a Newtonian
fluid. A typical
household product
will help illustrate
this point, try
the following experiment.
Make a solution
of corn starch and
water, approximately
1 part water to
2 parts cornstarch.
Mix well into a
large shallow bowl.
Try moving this
fluid rapidly around
with your fingers.
The faster you try
to move through
the fluid, the higher
the resistance.
If you move your
fingers fast enough
they will skip over
the surface. At
that rate of shear,
the solution almost
behaves as a solid,
when the fingers
are moved slowly,
the solution behaves
more as expected
offering little
resistance. Compare
this behaviour to
another fluid that
seems equally thick,
such as molasses
(molasses is not
considered a Newtonian
fluid, however it
is much closer to
being Newtonian
than a starch solution).
The molasses flows
readily no matter
how fast the movement.
This is what is
meant by viscosity
being dependant
on rate of shear.
Why
do I care? Many
fluids that we
deal with are
Newtonian, but
not as many as
you might think.
I put together
a list (see book),
the data was not
easy to find.
I would appreciate
references for
any good sources
on this subject.
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5.4
Laminar flow
is a very well behave
flow usually occurring
at low speeds for
most fluids. In
the laminar flow
regime it is possible
to determine theoretically
the speed of any
particle between
the center of a
pipe and the wall.
Most fluids have
to be carried at
a much higher velocity
which puts them
in the turbulent
flow regime. For
turbulent flow,
the fluid particles
move in many directions,
each particle reacts
with its neighbor
in an unpredictable
fashion creating
much higher internal
friction than is
present in the laminar
flow situation.
If you put dye in
a laminar flow system,
you will observe
nice long streams
of dye undisturbed
by the surrounding
liquid. The same
dye inserted in
a turbulent flow
will immediately
be dispersed through
out the liquid.
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