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LMNO Engineering, Research, and Software, Ltd. |

Index to all Newsletters LMNO Engineering home page
LMNO@LMNOeng.com |

1999

December 14, 1999. Focus on Steady Pressurized Pipe Flow

November 30, 1999. Focus on Java Applets

November 9, 1999. Focus on Detention Storage to Attenuate
Storm Discharge

October 18, 1999. Focus on Closed Conduit Flow Measurement
and Bernoulli equation

October 3, 1999. Focus on Open Channel Flow Measurement:
Rectangular Thin Plate Weirs

September 14, 1999. Focus on Open Channel Flow Measurement:
V-Notch Weirs

August 30, 1999. Focus on Flow Measurement - Orifice
Flowmeters in Pipes

August 19, 1999. Focus on Fundamental Flow Equations:
Bernoulli and Energy Equations

July 26, 1999. Focus on Hydrology

July 13, 1999. Focus on Ideal Gas Law and Molecular Weight

June 22, 1999. Focus on Flow Measurement - Orifice
Flowmeters in Pipes

June 15, 1999. Focus on Flow Measurement

June 8, 1999. Focus on Circular Culverts (not under
pressure)

May 23, 1999. Focus on Open Channel Flow - the Froude Number

May 5, 1999. Pricing

April 19, 1999. Focus on Fluid Property Definitions -
Viscosity

April 5, 1999. Focus on Pressurized Pipe Flow

March 22, 1999. Focus on Discharge from a Tank

March 10, 1999. Focus on Flow Measurement

March 1, 1999. Focus on Open Channel Flow

February 17, 1999. Focus on Pressurized Non-Circular
Ducts/Conduits

February 11, 1999. Focus on Pressurized Pipe Flow

LMNO Engineering, Research, and Software, Ltd.

The fluid flow calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. December 14, 1999

Focus on Steady Pressurized Pipe Flow

We receive many inquiries similar to, "What is the flowrate through a 6 inch diameter
horizontal pipe carrying water at 20 C at a pressure of 100 psi?" This question is
impossible to answer. Flowrate depends on a pressure difference. If the person had said,
"... pressure difference of 100 psi", then I could answer the question. A common
misunderstanding is that if pressure is known at one point in a pipe, then flowrate can be
determined - since somehow flowrate is proportional to pressure. The fact is that flowrate
is proportional to pressure difference.

Let's look at the energy equation for pipe flow between two locations that are a length
"L" apart. The constant diameter pipe carries an incompressible steadily flowing
fluid. There are no pumps or minor losses (valves, pipe bends, etc.) between points 1 and
2. The velocities at 1 and 2 are the same since the flow is steady, the fluid is
incompressible, and the diameters are the same. The governing equation reduces to:

(P_{1}-P_{2})/S = H

where P_{1}=upstream pressure [F/L^{2}], P_{2}=downstream pressure
[F/L^{2}],

S=weight density of fluid [F/L^{3}], H=major loss (also called friction loss) [L].

Note that S=dg where d=fluid density [M/L^{3}] and g=acceleration due to gravity
[L/T^{2}].

H is a function of velocity, pipe roughness, diameter, and length. It is commonly
represented by the Darcy-Weisbach friction loss equation (https://www.LMNOeng.com/DarcyWeisbach.htm)
or the Hazen-Williams friction loss equation (https://www.LMNOeng.com/HazenWilliamsDesign.htm).
After computing (P_{1}-P_{2})/S, velocity (and flowrate) can be found
using your preferred friction loss equation.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website. If you no
longer wish to receive it, send a message stating "Discontinue Newsletter" to
LMNO@LMNOeng.com.

(c) 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid flow calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. November 30, 1999

Focus on Java Applets

Usually our newsletter discusses technical aspects of fluid flow applications, such as the
Bernoulli equation, pipe flow, open channel flow, flow measurement, or runoff during a
storm. This newsletter is going to discuss some thoughts related to the calculations we
write and how they run on the web.

Our calculations are written using the Java programming language. Java is a very good
language for us to use since, when compiled into a "*.class" file, the resulting
file (called a "Java applet") can run on virtually any computer - from Macs to
PC's to servers. Java is called a "platform independent" language. When you load
one of our calculation pages, the calculation (Java applet) does not actually run on our
server, but rather (like the web page itself) downloads and runs on your PC. If you
connect to the internet using a telephone connection, you may have noticed that you can
continue to run web pages even after disconnecting. Your last few web pages are stored in
a temporary buffer on your PC or Mac.

There are some computers that seem to have trouble showing our calculations. I know of
someone who recently joined America On Line (AOL) and loaded Internet Explorer 4.0 (IE 4).
The lines in the calculations appeared to overlap each other. Have any of our newsletter
subscribers had this problem? If so, how did you resolve it? This is the only occurrence
of a problem we have heard of with IE 4 or AOL, which usually show and run our
calculations very well.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website. If you no
longer wish to receive it, send a message stating "Discontinue Newsletter" to
LMNO@LMNOeng.com.

(c) 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid flow calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. November 9, 1999

Focus on Detention Storage to Attenuate Storm Discharge

(https://www.LMNOeng.com/Hydrology/storage.htm)

Our newest addition to the LMNO Engineering website is a calculation for sizing detention
basins to attenuate peak discharge from a storm event.

Communities usually have guidelines stating that peak discharge at some location following
development cannot exceed the peak discharge prior to development. The
"location" is usually somewhere in the watershed where flooding would be
detrimental. Development usually involves clearing trees and brush, paving surfaces, and
constructing buildings. These activities tend to increase runoff volume and peak discharge
from the watershed.

Detention storage can be incorporated into developments to attenuate (reduce) the peak
discharge. For example, say a city requires the 25-yr, 24-hr storm to be the basis for
design. Prior to development, the peak discharge from this storm is, say, 150 cfs (ft3/s)
at a specified location, and the peak discharge due to development is predicted to be,
say, 300 cfs at the same location. The city won't approve the project unless the developer
incorporates enough detention storage to reduce the predicted peak discharge to the
pre-development value of 150 cfs at the specified location.

The engineer can use our calculation to determine the detention storage volume required to
attenuate the peak discharge from 300 to 150 cfs. The storage volume can then be
implemented as a single pond with that volume or several ponds, basins, or depressions
that add up to the required volume. The ponds/basins/depressions must go dry between storm
events and should be located just upstream of the specified location.

Our calculation is based on methodology presented in Technical Release 55, Chapter 6 (SCS,
1986), of the USA Soil Conservation Service (now called the Natural Resources Conservation
Service, NRCS), division of the USDA (USA Department of Agriculture). The NRCS has worked
for decades developing equations and conducting experiments to determine reliable models
for predicting storage volume for detention basins to reduce peak discharge from storm
events. We have made the calculation useful for the international community by allowing a
variety of units.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

Reference:

U.S. Soil Conservation Service. Technical Release 55: Urban Hydrology for Small
Watersheds. USDA (U.S. Department of Agriculture). June 1986. Available from NTIS
(National Technical Information Service), NTIS # PB87101580.

You received this free newsletter because you requested it at our website. If you no
longer wish to receive it, send a message stating "Discontinue Newsletter" to
LMNO@LMNOeng.com.

(c) 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid flow calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.comLMNO@LMNOeng.com

Newsletter. October 18, 1999

Focus on Closed Conduit Flow Measurement and Bernoulli equation

This newsletter will discuss pressure variation with distance through a differential
pressure flow meter, such as an orifice, nozzle, or venturi, carrying an incompressible
fluid (a liquid). The distinction between differential pressure and pressure loss will be
examined.

Differential pressure is the basis for determining the flowrate through one of these
devices. Differential pressure is equal to the pressure upstream of the device minus the
pressure at the throat of the device; these two locations are indicated on the diagrams on
our web pages. The overall pressure loss due to a nozzle or orifice is usually taken as
the pressure at one diameter upstream of the throat minus the pressure at a distance 6
diameters downstream of the throat (ISO, 1991); the pressure loss measurement locations
are intended to be beyond the range of influence of the device.

Differential pressure will be greater than pressure loss because the pressure at the
throat is much smaller than the pressure at 6D downstream. The throat pressure is low
because the throat has a reduced diameter resulting in high velocity. As velocity
increases, pressure decreases. This is in accordance with the Bernoulli equation for a
horizontal flowmeter: P + (d V^{2})/2 = constant, where P is pressure, d is liquid
density, and V is velocity. As V goes up, P goes down.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

Reference:

ISO (1991). International Organization of Standards. ISO 5167-1:1991(E). Measurement of
fluid flow by means of pressure differential devices - Part 1: Orifice plates, nozzles,
and Venturi tubes inserted in circular cross-section conduits running full. 1991.

You received this free newsletter because you requested it at our website. If you no
longer wish to receive it, send a message stating "Discontinue Newsletter" to
LMNO@LMNOeng.com.

(c) 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid flow calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. October 3, 1999

Focus on Open Channel Flow Measurement: Rectangular Thin Plate Weirs

https://www.LMNOeng.com/Weirs/RectangularWeir.htm

Thin plate weirs are typically installed in open channels such as streams to determine
discharge (flowrate). The basic principle is that discharge is directly related to the
water depth behind the weir. The rectangular weir is the most commonly used thin plate
weir.

Rectangular weirs can be "suppressed," "partially contracted," or
"fully contracted." Suppressed means there are no contractions. A suppressed
weir's notch width (b) is equal to the channel width (B); thus, there really isn't a notch
- the weir is flat all the way along the top. For a weir to be fully contracted, (B-b)
must be greater than 4h(max), where h(max) is the maximum expected head on the weir (USBR,
1997). A partially contracted weir has B-b between 0 and 4h(max). Weir contractions cause
the water flow lines to converge through the notch.

USBR (1997) provides equations for a "standard" fully contracted rectangular
weir and a "standard" suppressed weir. The U.S. Bureau of Reclamation has
conducted many weir tests over several decades using weirs with particular dimensions -
usually notch widths in 1 ft. increments up to about 10 ft. Therefore, any weir outside
their tested dimensions is non-standard, and their equations should not be used. To
provide a single accurate method to model all rectangular weirs (suppressed, partially
contracted, and fully contracted), the Kindsvater-Carter equation (Kindsvater and Carter,
1959) was developed. It is considerably more complex than the USBR standard weir
equations. However, USBR (1997) states that the Kindsvater-Carter method is at least as
accurate, if not more, than the standard weir equations for suppressed and fully
contracted weirs. And further, the Kindsvater-Carter equation reliably models partially
contracted weirs. ISO (1980), ASTM (1993), and USBR (1993) all recommend using the
Kindsvater-Carter method for all rectangular thin plate weirs. Our calculation utilizes
the Kindsvater-Carter equation.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

References:

ASTM (1993). American Society for Testing and Materials. ASTM D5242. Standard method for
open-channel flow measurement of water with thin-plate weirs. 1993.

ISO (1980). International Organization of Standards. ISO 1438/1-1980(E). Water flow
measurement in open channels using weirs and venturi flumes - Part 1: Thin plate weirs.
1980.

Kindsvater, C. E. and R. W. Carter. 1959. Discharge characteristics of rectangular
thin-plate weirs. Transactions, American Society of Civil Engineers. v. 24. Paper No.
3001.

USBR (1997). U.S. Department of the Interior, Bureau of Reclamation. Water Measurement
Manual. 1997. 3ed.

You received this free newsletter because you requested it at our website. If you no
longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid flow calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. September 14, 1999

Focus on Open Channel Flow Measurement: V-Notch Weirs

https://www.LMNOeng.com/Weirs/vweir.htm
(FREE Calculation - no password required)

Due to the large demand for flow measurement calculations, our latest addition to the LMNO
Engineering website is a calculation for V-notch weirs. V-notch (or triangular) weirs are
used for flow measurement in streams that are typically up to 10 ft. (3 m) wide. The weir
is like a dam which backs up the water, and the water depth flowing over the weir is
related to discharge. Our calculation solves for discharge and water depth (head);
computing head is useful for designing a weir. The calculation allows notch angles from 20
to 100 degrees. 90 degrees is the most common notch angle.

Other types of weirs frequently used are rectangular weirs and Cipoletti weirs. V-notch
weirs are used where discharge is not expected to change too much. The V-notch weir
provides a larger head change than a rectangular or Cipoletti weir for a given increase in
discharge. This allows a greater accuracy in the head measurement and thus the discharge.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website, or you are a
registered user. If you no longer wish to receive it, send a message stating
"Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid flow calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. August 30, 1999

Focus on Flow Measurement - Orifice Flowmeters in Pipes

https://www.LMNOeng.com/orifice.htm

Our orifice flowmeter calculation has been extended to compute flowrate and orifice
diameter. Previously, the calculation only computed differential pressure. Flowrate is
generally what professionals wish to compute, and it is computed based on a measured
differential pressure. However, if an orifice flowmeter is to be purchased, one must
decide on what diameter (or diameter ratio: orifice diameter/pipe diameter) the orifice
should have such that the device can cover the full range of expected flowrates.

Mathematical methods used to program the orifice calculations: The calculation for
differential pressure is analytic; that is, it has a straight-forward ("closed
form") solution. However, the flowrate and orifice diameter calculations require
numerical solutions since the Discharge Coefficient cannot be computed directly because it
depends on orifice diameter and flowrate. We have written a cubic solution method which
utilizes mathematical derivatives to solve for flowrate and diameter.

Try going to the web page and solving for differential pressure. Then, solve for flowrate;
you will get the same flowrate that was used to compute differential pressure. The program
appears just as fast in computing flow as pressure, but actually a lot more computations
occurred in the flowrate calculation.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website, or you are a
registered user. If you no longer wish to receive it, send a message stating
"Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid flow calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. August 19, 1999

Focus on Fundamental Flow Equations: Bernoulli and Energy Equations

In the USA, engineering students typically take a course in fluid mechanics during their
junior year (their 3rd year in a 4 year degree program) of college. In this course, they
learn one of the most fundamental equations of fluid mechanics - the Bernoulli equation.
The Bernoulli equation is valid for simulating internal and external flows. Internal flow
is flow inside a pipe or duct; external flow includes raindrops falling from the sky,
tennis balls rising from the bottom of a swimming pool, etc. However, the Bernoulli
equation is only valid when the situation is steady state, the fluid is incompressible and
inviscid (i.e. no friction between the fluid and the object or pipe wall), and flow is
along a streamline. In reality, no flow situation perfectly matches these criteria.

Even though the Bernoulli equation can only be used under ideal conditions, it is taught
because it is the precursor to the Energy equation. The energy equation (https://www.LMNOeng.com/energy.htm) is the
Bernoulli equation with one additional term - head loss. Head loss (also known as energy
loss) incorporates the effects of friction for internal flows (friction for external flows
is called "drag", which is a different topic). Since frictional effects are
accounted for, the energy equation is able to simulate almost all real internal steady
flows where the fluid is relatively incompressible. It is commonly used to predict
pressure loss in a long pipeline.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website, or you are a
registered user. If you no longer wish to receive it, send a message stating
"Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid flow calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. July 26, 1999

Focus on Hydrology (https://www.LMNOeng.com/Hydrology/hydrology.htm)

Our newest addition to the LMNO Engineering website will help you predict the maximum
discharge during a 24-hour storm event of whatever return period is important to your
situation (5-year, 25-year, 100-year, etc.). The calculation is based on methodology
presented in the U.S. Soil Conservation Service Technical Release 55 (known as TR-55)
published in 1986. It is also known as the "curve number" method.

The method is commonly used to compare peak discharges from identical storms before and
after land development. Often, land development results in wooded or agricultural areas
being replaced by parking lots, roads, and buildings. These cause an increase in the peak
discharge since there is more (and faster) runoff and less infiltration. This will cause
increased flooding if the stream overflows its banks.

Our calculation has many nice features including a variety of units, the ability to enter
five different curve numbers and their representative areas, a time of concentration
calculator, and links to precipitation maps.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website, or you are a
registered user. If you no longer wish to receive it, send a message stating
"Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid mechanics calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. July 13, 1999

Focus on Ideal Gas Law and Molecular Weight

Since our last newsletter, LMNO Engineering has added calculations for the Ideal Gas Law
and molecular weights. In the field of fluid mechanics, the ideal gas law is useful for
determining the density of a gas based on pressure and temperature. Gas flow through pipes
can be simulated using the calculation "Design of Circular Liquid or Gas Pipes;"
it uses the Darcy-Weisbach friction loss equation. Even though the calculation is for
constant density fluids, gases are commonly simulated if their pressure (thus density) is
fairly constant over the pipe length of interest.

We have also written a molecular weight calculator which is a general use (free) program.
It may be especially useful to environmental specialists who need to determine the
molecular weight of a particular compound.

We are currently working on additional features for the orifice, nozzle, and venturi
calculations (solve for flowrate and diameter). We are also beginning work on flow
measurement calculations for water flow over various types of weirs (v-notch, rectangular,
and Cipoletti). Following flow measurement, the next category receiving the most interest
on our home page questionnaire is hydrology. We will soon begin work on a
rainfall-runoff/peak discharge calculation based on the U.S. Soil Conservation Service
Technical Report 55 (1986).

As always, we appreciate your suggestions for additional calculations.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website, or you are a
registered user. If you no longer wish to receive it, send a message stating
"Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid mechanics calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. June 22, 1999

Focus on Flow Measurement - Orifice Flowmeters in Pipes

https://www.LMNOeng.com/orifice.htm

Our last newsletter announced calculations for venturi and nozzle flowmeters. Now, the
LMNO Engineering website additionally has an orifice flowmeter calculation. The
calculation uses equations published in the ISO 5167-1 (1991, 1998) international standard
(ISO is the International Standards Organization). Venturi, nozzle, and orifice meters are
used for determining flowrate through a pipe flowing under pressure. Differential pressure
across the flowmeter is measured, then the flowrate is computed using detailed empirical
equations.

The ISO standard covers three different types of orifices which are distinguished from
each other by the locations of their upstream and downstream pressure taps. Orifice
diagrams and equations are shown on our orifice web page along with the calculation. The
orifice equations are valid for a wider range of Reynolds numbers than nozzle or venturi
equations. Orifices can be used in pipes from 5 cm to 1 m diameter and Reynolds numbers up
to infinity.

Currently, our calculations only solve for the differential pressure measured across the
orifice based on a known flowrate - useful for pressure gage selection for an application.
If you need to know flowrate based on a differential pressure reading, you can enter
various flowrates until the output differential pressure is the value on your pressure
gage. We are currently working on calculations to solve directly for flowrate.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website, or you are a
registered user. If you no longer wish to receive it, send a message stating
"Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid mechanics calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. June 15, 1999

Focus on Flow Measurement

Since our last newsletter, LMNO Engineering published two new calculations on the website:
Flow measurement using venturi and nozzle flow meters. These calculations simulate flow of
liquids through venturi and nozzle flow meters in pipes flowing full with 5 cm to 1 m
diameters. The calculations are based on equations published in the ISO 5167-1
international standard. Venturis and nozzles are two of the most commonly used devices for
fluid flow measurement in pipes. Venturis have less pressure loss but tend to be more
expensive than nozzles. Currently, our calculations only solve for the differential
pressure measured across the venturi or nozzle based on a known flowrate. If you need to
know flowrate based on a differential pressure reading, you can enter various flowrates
until the output differential pressure is the value on your pressure gage. We are
currently working on calculations to solve for flowrate. We are also working on
calculations for orifice flow meters, another common flow measurement device.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website, or you are a
registered user. If you no longer wish to receive it, send a message stating
"Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid mechanics calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. June 8, 1999

Focus on Circular Culverts (not under pressure)

Take a look at the equations in Design of Circular Culverts (https://www.LMNOeng.com/CircularCulvert.htm)
or Geometry of Circular Culverts (https://www.LMNOeng.com/circular.htm).
We have had some inquiries about an apparent inconsistency in the units of the angle
theta. For this newsletter, let "a" represent the angle theta since the Greek
letter theta cannot be sent via email. Look at the equation for flow area, A=d^{2}
[a-sin(a)] / 8. The first "a" must be in radians; whereas, the "a"
inside the sin term can be in radians or degrees so long as the computer (or your
calculator) is told which units "a" is in. Our calculation shows "a"
in degrees because most USA engineers and scientists tend to visualize degrees more easily
than radians (this may not be true elsewhere in the world). Our calculation converts
between degrees and radians as required. The conversion is PI radians=180 degrees, where
PI is 3.1415927. The Java programming language has a built-in function for PI which has
even more decimal places.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website, or you are a
registered user. If you no longer wish to receive it, send a message stating
"Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid mechanics calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. May 23, 1999

Focus on Open Channel Flow - the Froude Number

The Froude number (Fr) is computed on our Open Channel Flow calculation pages. Fr=V/(gy)^{1/2}
where V=water velocity [L/T], g=acceleration due to gravity [L/T^{2}], and y=water
depth [L]. It was developed over 50 years ago as a dimensionless parameter relating
inertial forces to gravitational forces. Flows with Fr<1 are called
"sub-critical," Fr=1 are called "critical," and Fr>1 are called
"super-critical." Fr is a useful parameter for describing open channel flows. If
a flow is super-critical, it is moving rapidly - so rapidly that the water velocity is
faster than the wave velocity. Waves in super-critical flows cannot move upstream.
However, waves in sub-critical flows can move upstream. The relative velocity of water
versus waves impacts the use of controls in channels - such as dams, culverts, flumes, and
weirs. For a weir or flume to be a useful flow measurement device, Fr must be <1
upstream of the weir or flume so that critical flow can occur at the weir or flume. When
critical flow occurs, there is a direct relationship between velocity (thus discharge) and
water depth.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website, or you are a
registered user. If you no longer wish to receive it, send a message stating
"Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid mechanics calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. May 5, 1999

LMNO Engineering is planning to raise its prices for the password-protected features of
the website. We will soon be able to accept payments by credit cards in addition to our
previous method of checks or money orders. Our new prices will go into effect sometime
after May 19, 1999. We will have numerous payment options (site licenses and durations and
possibly reduced fees for access to individual portions of the site). A sampling of the
new prices are:

Access to the entire website for 7 days (5 computers): $8 (US Dollars)

Access to the entire website for 30 days (5 computers): $20

Access to the entire website for 7 days (30 computers): $35

Under the new system, your web browser must have "cookies" turned on. Any
browser that can run our calculations has an option to turn cookies on or off. If you are
averse to cookies, you may turn cookies off after our website sends a cookie to your
computer.

Until we institute our new prices, our current fee of $2 per month will remain in effect:
$2 will allow access through June 30, 1999. $14 will allow access through December 31,
1999. $26 will allow access through June 30, 2000. So, subscribe by May 19 to take
advantage of our current pricing. Payments should be sent to the address at the top of
this newsletter. International users can send checks drawn on their local bank for the
equivalent of US Dollars.

Thank you for your interest in the LMNO Engineering website,

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website, or you are a
registered user. If you no longer wish to receive it, send a message stating
"Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid mechanics calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. April 19, 1999

Focus on Fluid Property Definitions - Viscosity

Ever wondered what the difference is between dynamic viscosity and kinematic viscosity?
Take a look at our Fluid Properties page (https://www.LMNOeng.com/fluids.htm).
The greek letter v ("nu") is kinematic viscosity. It has generic units of [L^{2}/T]
where L means length and T means time. The British Gravitational (BG) units and SI
(International System) units are ft^{2}/s and m^{2}/s, respectively. Have
you heard of dynamic viscosity? Usually, the greek letter µ ("mu") is used to
indicate dynamic viscosity. Dynamic viscosity is also known as absolute viscosity. v=µ/p
where the greek letter p ("rho") is fluid density. The units of dynamic
viscosity are [M/(L-T)] (M means mass; the "-" means "multiplied by,"
not minus) with typical units being slug/ft-s or kg/m-s. A slug is the BG unit for mass.
Other units for kinematic viscosity are centistoke and stoke. Other units for dynamic
viscosity are centipoise and poise.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website, or you are a
registered user. If you no longer wish to receive it, send a message stating
"Discontinue Newsletter" to LMNO@LMNOeng.com.

© 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid mechanics calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. April 5, 1999

Focus on Pressurized Pipe Flow

In a past Newsletter, we discussed some of the differences between the Hazen-Williams (HW)
and Darcy-Weisbach (DW) major loss equations. If you have gotten on the website in the
last few days, you may have noticed that we added three calculations to Design of Circular
Liquid or Gas Pipes (https://www.LMNOeng.com/DarcyWeisbach.htm).
They are "Solve for V, Q", "Q known. Solve for Diameter," and "V
known. Solve for Diameter." If you have taken a fluid mechanics course, then you may
remember the first as being called a Type II problem and the last two as called Type III
problems. Solving a Type II or III problem by hand is not a straight-forward calculation.
Many iterations between the energy equation and the Moody diagram are required. Our
numerical solutions for Type II and III problems should save you a lot of time. Recall
that the DW equation is valid for any liquid or gas while the HW equation is only valid
for water at typical water supply temperatures.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website, or you are a
registered user. If you no longer wish to receive it, send a message stating
"Discontinue Newsletter" to LMNO@LMNOeng.com.

© 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid mechanics calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. March 22, 1999

Focus on Discharge from a Tank

One of our users inquired about how to increase the discharge from a tank by pressurizing
the head space above the water in the tank. He was using the Discharge from a Tank
calculation (https://www.LMNOeng.com/TankDischarge.htm)
which is listed under Flow Measurement. Since the calculation assumes the top of the tank
is open to the atmosphere, how do you account for the additional tank pressure? Let's look
at the free discharging orifice (as opposed to the submerged orifice). H is the distance
shown in the figure on the calculation page. The equation to use is H=h_{1}+h_{2}.
Let h_{1} be the depth of water above the orifice. Let h_{2}=P/S where P
is the head pressure (gage pressure; not absolute pressure) in the tank and S is the
weight density of the water in the tank (also known as specific weight). If P=0, then H=h_{1}
as expected for a tank open to the atmosphere. Let's look at an example. If h_{1}=3
ft. and P=5 psig (pounds per square inch, gage pressure), then h_{2} = (5 lb/in^{2})(144
in^{2}/ft^{2})/(62.3 lb/ft^{2})=11.6 ft. 62.3 is S for water at 70
F. If your water has a different temperature, use S for your temperature (but it won't be
very different). Therefore, H=3 + 11.6 = 14.6 ft. You can also use the calculation
backwards: Enter the discharge that you need and the calculation will compute H. Then,
determine P based on your h_{1}.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website, or you are a
registered user. If you no longer wish to receive it, send a message stating
"Discontinue Newsletter" to LMNO@LMNOeng.com.

© 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid mechanics calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. March 10, 1999

Focus on Flow Measurement

Visitors to our website have indicated that they would like to see flow measurement
calculations. Flow measurement received three times as many votes on our home page as any
other category listed. We have recently published our first of several flow measurement
calculations. It is called Discharge from a Tank (https://www.LMNOeng.com/TankDischarge.htm).
This calculation may be used to simulate water flowing from a tank to the atmosphere
through a circular or square orifice. Lots of information can be computed and/or input
including information about the water's trajectory (path) as it leaves the tank. The
calculation may also be used to simulate water flowing through a submerged orifice.
"Submerged orifice" means that the water depth is at least up to the top of the
orifice on the downstream side. Note that trajectory information for a submerged orifice
has no meaning. In the future, we will publish calculations to simulate venturi, nozzle,
and orifice flowmeters in pressurized pipes.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website, or you are a
registered user. If you no longer wish to receive it, send a message stating
"Discontinue Newsletter" to LMNO@LMNOeng.com.

© 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid mechanics calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. March 1, 1999

Focus on Open Channel Flow

The Manning Equation (https://www.LMNOeng.com/manning.htm)
is the most commonly used equation to analyze open channel flows. The Manning Equation is
utilized in our open channel design calculations for circular culverts (https://www.LMNOeng.com/CircularCulvert.htm)
and rectangular channels (https://www.LMNOeng.com/water.htm).
The Manning Equation is a semi-empirical equation for simulating water flows in channels
and culverts where the water is open to the atmosphere (not flowing under pressure). The
equation was first presented in 1889 by Robert Manning, an Irish engineer. The units in
the Manning Equation appear to be inconsistent; however, the value k has hidden units in
it to make the equation consistent. The Manning Equation was developed for uniform steady
state flow. Uniform means that the channel is prismatic. Prismatic means the channel has
constant dimensions (including depth) along its length. Steady state means the flowrate,
velocity, and everything else are constant with time. In reality few flows strictly meet
these conditions. However, for individual channel reaches (e.g. one mile of a 200 mile
river) the assumptions may be fairly well achieved.

In the Manning Equation,

S is the slope of the water surface or the slope of the channel bottom: Elevation change
divided by length of reach. For uniform flows, the water surface has the same slope as the
channel bottom since the water depth is constant with channel length.

P is the wetted perimeter. It is the contact length between the water and the channel. For
example, for a circular culvert flowing half full, P would be half the culvert
circumference.

n is the Manning roughness coefficient. It depends on the channel material. Values for n
can be found at https://www.LMNOeng.com/manningn.htm.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website, or you are a
registered user. If you no longer wish to receive it, send a message stating
"Discontinue Newsletter" to LMNO@LMNOeng.com.

© 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid mechanics calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. February 17, 1999

Focus on Pressurized Non-Circular Ducts/Conduits

On February 14, we published a new calculation on the website called "Non-Circular to
Circular Pipe Conversions" at https://www.LMNOeng.com/PipeDuct.htm.
This calculation allows one to use the circular pipe design calculations ("Design of
Circular Water Pipes" and "Design of Circular Liquid and Gas Pipes") for
non-circular cross-sections. If you have a rectangular or annular cross-section, the new
calculation will convert your geometry to an equivalent diameter (called hydraulic
diameter) which can then be used in the circular design calculations to predict velocity.
However, to calculate the flowrate, take the velocity from the design calculation page and
copy it to the new calculation page so that the velocity is multiplied by the actual duct
area. This will give the correct flowrate. The flowrate output in the design calculation
is computed as VA where A=(pi/4)D^{2}, which is incorrect for a non-circular
cross-section. Even though the D is the hydraulic diameter, (pi/4)D^{2} is not
equal to the area computed from the actual duct geometry. Type some sample numbers in the
new calculation to prove it to yourself, then compare the calculation's area to (pi/4)D^{2}
using your calculator. The new calculation is free (not password-protected).

Conversely, if you use "Design of Circular Water Pipes" to determine a pipe
diameter based on a required velocity, the new calculation can be used to convert the
diameter to a height and width of a rectangular duct or an inner and outer diameter for an
annular cross-section. For the same reasons as in the previous paragraph, the circular
pipe design calculations cannot be used to compute hydraulic diameter based on flowrate,
since A=(pi/4)D^{2} is used.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website, or you are a
registered user. If you no longer wish to receive it, send a message stating
"Discontinue Newsletter" to LMNO@LMNOeng.com.

© 1999 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

The fluid mechanics calculations website: https://www.LMNOeng.com

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614

LMNO@LMNOeng.com

Newsletter. February 11, 1999

Focus on Pressurized Pipe Flow

When should I use "Design of Circular Liquid or Gas Pipes" versus "Design
of Circular Water Pipes"? Both of these calculations are for flows under pressure in
a circular pipe. The first one uses the Darcy-Weisbach friction (major) loss equation
which is valid for any liquid or gas. The user must enter the fluid so that the
appropriate viscosity and density are used. The second calculation is only valid for water
between 40 and 75F because friction losses are based on the empirical Hazen-Williams
equation. The Hazen-Williams equation was developed (decades ago) only for water. Both
equations give roughly the same results for water. You might want to try calculating
elevation difference using both calculations and compare them. Just enter any numbers (the
same for both calculations), compute Z_{1}-Z_{2}, and see how close the
two calculations are. Be sure to use the same scenario for both calculations.

Currently, "Design of Circular Liquid or Gas Pipes" does not compute velocity,
flowrate, or diameter (these have to be entered). We are working on adding these features,
and they will be implemented within 30 days.

Thank you for your interest in the LMNO Engineering website.

Newsletter written by Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this newsletter because you requested it at our website, or you are a
registered user. If you no longer wish to receive it, send a message stating
"Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 1999 LMNO Engineering, Research, and Software, Ltd.

**© 1999-2023 LMNO Engineering, Research, and Software, Ltd. (All
Rights Reserved)**

LMNO Engineering, Research, and Software, Ltd.

7860 Angel Ridge Rd. Athens, Ohio USA (740) 707-2614

LMNO@LMNOeng.com https://www.LMNOeng.com