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LMNO Engineering, Research, and Software, Ltd. |

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

2000

December 5, 2000. Bernoulli Equation Calculator

November 20, 2000. Bernoulli Equation

October 31, 2000. Pump Curves

October 18, 2000. Trapezoidal Open Channels

September 26, 2000. EGL and HGL: Energy Grade Line and
Hydraulic Grade Line

September 8, 2000. End Depth Method for Flow Measurement in
Open Channels

August 22, 2000. New Calculations

July 31, 2000. Recent Additions to Fluid Flow Calculations
Website

July 10, 2000. Focus on Units - Pounds (force) and Pounds
(mass)

June 14, 2000. Focus on Water Hammer

May 31, 2000. Focus on Water Hammer

May 9, 2000. Focus on Flow Measurement using Venturis,
Nozzles, and Orifices in pipes flowing full.

April 21, 2000. Focus on Gas Flow Measurement using an
Orifice

March 28, 2000. Focus on Hydrology (Rainfall-Runoff)

March 8, 2000. Focus on Groundwater Flow Direction and
Gradient

February 22, 2000. Free Password for LMNO Engineering website

February 5, 2000. Focus on Groundwater Contaminant Transport

January 21, 2000. Focus on Groundwater

January 6, 2000. Focus on Moody Diagram

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. December 5, 2000

Bernoulli Equation Calculator

http://www.LMNOeng.com/Flow/bernoulli.htm

As promised, our Bernoulli equation calculator is now up and running. We have simplified
the use of the Bernoulli equation by having some applications built into the program.
Otherwise, there is often confusion about whether velocity at location 1 or 2 should be
set to zero, or pressure at location 1 or 2 should be zero and so on.

In our calculation, you can select pitot tube, pitot tube in a circular or non-circular
conduit, flow over a dam, flow under a sluice gate, leak rate from a pipe, flow from a
tank into a pipe, pipe expansion/contraction; or venturi, nozzle, or orifice flowmeter.
All of the applications are explained on the web page. You may solve for flowrate (and
velocity), pressure, elevation, or geometry.

You may be aware that our website already has calculations for venturi, nozzle, and
orifice flowmeters based on the rigorous ISO 5167 method. The Bernoulli calculator
provides a less accurate solution but is not limited to certain pipe diameters, throat
diameters, or Reynolds numbers. The ISO 5167 equations are only valid for certain ranges
of diameters and Reynolds numbers.

Thank you for your interest in the LMNO Engineering website, http://www.LMNOeng.com

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

Reference

International Organization of Standards (ISO 5167-1). 1991, 1998. 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. Reference number:
ISO 5167-1:1991(E) and Amendment 1:1998(E).

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) 2000 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. November 20, 2000

Bernoulli Equation

According to "Fundamentals of Fluid Mechanics" by Munson, Young, and Okiishi
(1998), the Bernoulli equation is "the most used and abused equation in fluid
mechanics." The Bernoulli equation can be used for analyzing many applications such
as pitot tube, pipe diameter change, dam, sluice gate, discharge from a tank, leakage from
a pipe, and differential pressure flowmeters. However, many of these applications require
additional empirical factors to be used with the Bernoulli equation in order to obtain
satisfactory results.

The Bernoulli equation is strictly only valid when the following conditions are met:
incompressible and inviscid fluid, steady flow, and flow along a streamline. In reality,
no fluid is inviscid (all fluids have viscosity). Liquids are essentially incompressible
and gases are incompressible if undergoing only small pressure changes. Steady flow can be
reasonably achieved. Determining a streamline in which to analyze the flow along is
physically nearly impossible, yet the Bernoulli equation can still be used effectively
without strictly knowing its streamline.

We have a free calculation called the Energy Equation http://www.LMNOeng.com/energy.htm. If the
head loss is zero, then the equation shown is called the Bernoulli equation. Head loss of
zero indicates that viscous effects are negligible. By the time we send our next
newsletter, we expect to have completed a comprehensive Bernoulli equation calculator
where you can select an application - such as pitot tube, pipe expansion, flow from a
tank, leakage from a pipe, dam, sluice gate, flowmeter, etc. - and compute flowrate,
velocity, pressure difference, elevation difference, or diameter (or area or channel
width).

Thank you for your interest in the LMNO Engineering website, http://www.LMNOeng.com

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

Reference

Munson, B. R., D. F. Young, and T. H. Okiishi. Fundamentals of Fluid Mechanics. John Wiley
and Sons, Inc. 1998 (3ed), p. 103.

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) 2000 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. October 31, 2000

Pump Curves

http://www.LMNOeng.com/Pipes/HWpump.htm

As promised, our pump curve program is now up and running. It is similar to our
Hazen-Williams water pipe design calculation, but includes an equation for a pump curve. A
pump curve is obtained from a pump manufacturer and is a plot of head supplied by the pump
vs. pump capacity. Capacity is also known as flowrate or discharge. Larger pumps can
provide more flow against greater head requirements than smaller pumps, so it is
economical to select the smallest pump that satisfies your needs.

Some pump catalogs provide entire graphs of head vs. capacity for their various pumps
while other catalogs only list two points on the pump curve and don't show the curve. The
two points are usually the maximum capacity that the pump can provide (which occurs at
zero head) and the maximum head that the pump can provide (which occurs at zero flow).

To make our calculation useful for the greatest number of users, we require you to input
only the two points on the pump curve described above. Then, our calculation forms a pump
curve in the shape of a parabola between the two points. Most centrifugal pump curves are
parabolic in shape, so this is a reasonable approximation. Please visit the pump curve web
page for a graph showing a parabolic pump curve formed from two points: http://www.LMNOeng.com/Pipes/HWpump.htm

Thank you for your interest in the LMNO Engineering website, http://www.LMNOeng.com

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) 2000 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. October 18, 2000

Trapezoidal Open Channels

Our newest calculation simulates flow in an open channel having a trapezoidal
cross-sectional geometry. Flow is simulated using the Manning equation which has been
discussed in previous newsletters.

Trapezoidal geometries are engineered in many man-made channels, and many natural channels
can be approximated as trapezoidal. Our calculation allows you to enter 30 different
combinations of inputs - whether you are solving for discharge based on depth, bottom
width, or top width. Or, if you are designing a channel depth, bottom width, or top width
to carry a desired discharge or velocity. The calculation can also predict channel slope
and Manning's channel roughness coefficient.

If you are more interested in flow in pressurized pipes rather than open channels, our
next newsletter will discuss a calculation we are currently completing - flow in pipes
under pressure with a pump curve. We have had many visitors ask for pump curves in
calculations and a newsletter about pumps and pump curves.

Thank you for your interest in the LMNO Engineering website http://www.LMNOeng.com

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) 2000 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. September 26, 2000

EGL and HGL

Two concepts that confound many students of hydraulics are EGL and HGL: Energy grade line
and hydraulic grade line. Simply put, these are plots of total head and hydraulic head
versus location along a pipeline.

Total Head (TH) is the sum of three terms: Elevation head + Pressure head + Velocity head.

Hydraulic Head (HH) is the sum of two terms: Elevation head + Pressure head.

Hydraulic head is also known as Piezometric head.

Head has units of energy per unit weight (i.e. force) of fluid. Since energy has units of
force times length, head is most often presented in units of length (FxL/F=L).

If a pipe flow system has head losses (due to friction between the pipe walls and the
fluid, and due to valves, bends, contractions, expansions etc.), then TH decreases. If a
piping system contains a pump, then TH will increase across the pump. Note that:

TH_{1} + Pump Head = TH_{2} + Losses, so that TH_{2} can be
computed as:

TH_{2} = TH_{1} + Pump Head - Losses

And for Hydraulic Head:

HH_{2} = TH_{2} - Velocity Head at 2 = TH_{1} + Pump Head - Losses
- Velocity Head at 2

where location 1 is upstream of location 2.

More information on the Energy equation can be found at http://www.LMNOeng.com/energy.htm.

Thank you for your interest in the LMNO Engineering website http://www.LMNOeng.com

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) 2000 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. September 8, 2000

End Depth Method for Flow Measurement in Open Channels

Ever wish you could determine the discharge (Q) of water out of a culvert? Maybe you
thought about using Manning's equation - but you needed to measure the slope and estimate
the Manning coefficient (n). And you realized that a small error in estimating n can give
a large error in Q. Maybe you found Q by measuring the time to fill a 20 liter bucket. For
high flows, the time is too short to measure accurately; and larger buckets get too heavy.

The end depth method doesn't require a slope measurement or an estimation of n. It is
based solely on the water depth (h) and diameter (D) of the culvert. It requires that the
culvert be essentially horizontal and that the water drops off a height greater than h.

We now have end depth calculations for circular culverts, rectangular channels, and
triangular channels that have sudden drop-offs (like a waterfall). The rectangular and
triangular channel calculations are fully functional without paying our registration fee.
You can see the rectangular channel calculation at http://www.LMNOeng.com/Waterfall/waterfall.htm.

Thank you for your interest in the LMNO Engineering website http://www.LMNOeng.com

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) 2000 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. August 22, 2000

New Calculations

We have had many requests for storage tank volume calculations. We now have a calculation
to determine the volume of a partially filled cylinder on its side, a partially filled
sphere and a cone frustum, which is a flat-topped cone. You can find these under the
"Volume Calculations" category on our home page. As usual, we have included many
different units and show the equations.

We also are in the final stages of testing a new open channel flow calculation which will
be ready by August 24. The calculation is based on equations in ISO 4371 and computes
discharge from measuring the water depth in a rectangular channel that drops off like a
waterfall.

Thank you for your interest in the LMNO Engineering website http://www.LMNOeng.com

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) 2000 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. July 31, 2000

Recent Additions to Fluid Flow Calculations Website

Since our last newsletter, we have added more units to Design of Circular Culverts and
Design of Rectangular Channels. We also have added an additional credit card processing
company for accepting payments.

Previously, Circular Culverts and Rectangular Channels accepted only meter and seconds
units or feet and seconds units. Now, they both accept more length and discharge units.
Length units now include cm, m, inch, and ft while discharge can be in m^{3}/s, ft^{3}/s
(cfs), gal/min (gpm), gal/day (gpd), and Acre-ft/yr.

Internet Billing Co., Ltd. (ibill), previously was the only credit card processing company
that we utilized. We continue to use ibill but now we also use PayPal. ibill is still the
best processor we have found that allows worldwide users to instantly obtain a PIN
(password) for our site, though its service is limited to three payment options. PayPal
currently only works for USA residents but has the advantage of accepting credit card
payment for tangible software purchasing as well as a password for the website for any
duration (7 days up to 1 year) and number of users.

Thank you for your interest in the LMNO Engineering website http://www.LMNOeng.com

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) 2000 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. July 10, 2000

Focus on Units - Pounds (force) and Pounds (mass)

We often receive questions such as, "What is pounds (force) and pounds (mass)."
Though this question may not present a problem to some of our readers, it is perplexing to
others. Let Lb_{f} represent pounds force and Lb_{m} represent pounds
mass. If you only use the metric system, then you never need to worry about Lb_{f}
and Lb_{m}. However, for those who work with English units, Lb_{f} and Lb_{m}
are often troublesome.

Lb_{m} is an inconsistent unit. It is not consistent with British Gravitational
(BG) Units or US Customary (USC) Units. BG (and USC) units use Lb_{f}, slugs,
feet, and seconds. Slug is the unit of mass. 1 Lb_{f} = 1 slug-ft/s^{2}.
The BG unit for mass density is slug/ft^{3}. Many engineers use Lb_{m}/ft^{3}
for density, however, which is not a BG unit but rather an English Engineering (EE) unit.

As an example, let's determine the hydrostatic water pressure 10 ft. below the surface of
a freshwater lake. For simplicity, assume the lake has a uniform temperature of 60F. The
equation for pressure is P=dgh, where P is pressure, d is water density, g is acceleration
due to gravity, and h is vertical distance below the water surface. g=32.174 ft/s^{2}
and h=10 ft. Using the BG system, d=1.94 slug/ft^{3} for water at 60F.

Therefore, P=(1.94 slug/ft^{3})(32.174 ft/s^{2})(10 ft)(1 Lb_{f}-s^{2}/slug-ft)=624
Lb_{f}/ft^{2}.

For those of you who use Lb_{m} a lot (the EE system), you might be tempted to use
d=62.4 Lb_{m}/ft^{3} at 60F. Then

P=(62.4 Lb_{m}/ft^{3})(32.174 ft/s^{2})(10 ft)=20,077 Lb_{m}/ft-s^{2},
which is not a pressure unit and is an incorrect use of units.

You can still use the 62.4 Lb_{m}/ft^{3}, but it must be used in a
different way.

Note that 32.174 Lb_{m} = 1 slug. Therefore, d=(62.4 Lb_{m}/ft^{3})/(32.174
Lb_{m}/slug)=1.94 slug/ft^{3}.

Therefore, P=(1.94 slug/ft^{3})(32.174 ft/s^{2})(10 ft)(1 Lb_{f}-s^{2}/slug-ft)=624
Lb_{f}/ft^{2}, which is correct.

You might think that all I did was take the 62.4, divide by 32.174, then multiply by
32.174. Well, you are right. 1 Lb_{f} = 1 Lb_{m} numerically, though Lb_{f}
is a force unit and Lb_{m} is a mass unit. You can think of 62.4 Lb_{m}/ft^{3}
as equivalent to 62.4 Lb_{f}/ft^{3}. But don't use it as a mass density;
use it as a weight density. Therefore, write the pressure equation as P=wh, where w=weight
density.

Therefore, P=(62.4 Lbf/ft^{3})(10 ft)=624 Lb_{f}/ft^{3}, which is
correct.

Thank you for your interest in the LMNO Engineering website http://www.LMNOeng.com

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) 2000 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. June 14, 2000

Focus on Water Hammer

http://www.LMNOeng.com/WaterHammer/WaterHammer.htm

Last issue, I presented the topic of water hammer. Now I would like to introduce our water
hammer calculation - the latest addition to the LMNO Engineering website. Our water hammer
calculation computes the maximum and minimum pressures in each pipe in a pipeline as well
as the time and location at which they occur. It is not limited to water; other liquids
can be used.

The calculation simulates water hammer in a pipeline flowing full, bounded upstream by a
large reservoir and bounded downstream by a valve which discharges to the atmosphere. The
reservoir is assumed to be large enough to absorb changes in pressure and remain at the
same elevation during the transient. There can be up to three pipes in series having
different lengths and diameters but the same pipe material. The time to close (or open)
the valve is entered. Also, the calculation allows you to enter an intermediate time and %
open so that the valve curve can be represented by two piece-wise linear equations, rather
than a step function or single linear function. If the valve is being closed, you must
also enter the initial (time=0) minor loss coefficient (K) for the valve.

Further discussion and equations can be found on the web page indicated above free of
charge. For the calculation to completely operate, our usual fee of $8 (US Dollars) is
required. Payment can be made by credit card at http://www.LMNOeng.com/register.htm - you
will instantly be given a password that fully enables the 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. If you no
longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 2000 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. May 31, 2000

Focus on Water Hammer

Water hammer is the increase or decrease in pressure in a pipeline due to rapidly changing
a valve or pump setting. The effects can be devastating. Pressure can rise well over twice
the steady state pressure in a pipeline due to a rapid valve closure causing a pipe to
burst. Water can suddenly vaporize due to opening a valve too quickly. Vaporization occurs
when the pressure in the pipe drops to the vapor pressure of water. This can result in
severe erosion of pipe surfaces.

Valve operation procedures usually indicate minimum closure (or opening) times to avoid
effects of water hammer. The equations governing water hammer rely on the wave speed of
water, mass conservation, and momentum conservation. Wave speed is a function of liquid
and pipe properties, including pipe diameter and wall thickness. To determine the maximum
and minimum pressures along a pipeline (and when and where they occur), a numerical
solution to the equations is necessary. We expect to have a water hammer calculation
completed by the time our next newsletter is sent.

Thank you for your interest in the LMNO Engineering website.

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

Additional reading:

Chaudhry, M. Hanif. 1986. Applied hydraulic transients. Van Nostrand Reinhold Co. 2ed.

Wylie, E. Benjamin and Victor L. Streeter. 1978. Fluid transients. McGraw-Hill Book Co.

Fox, J. A. 1989. Transient flow in pipes, open channels, and sewers. John Wiley and Sons.

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) 2000 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. May 9, 2000

Focus on Flow Measurement using Venturis, Nozzles, and Orifices in pipes flowing full.

Last issue, I introduced our orifice calculation for determining gas flowrate, diameter,
or pressure differential in pipes flowing full. I mentioned that the gas flow calculation
includes a factor called "expansibility" which accounts for the density change
of the gas as it flows through the orifice. For liquid flows, there is no density change.
Thus, the liquid flow equations for orifices are slightly simpler than the gas flow
equations.

Like orifices, gas flow through nozzles also involves density change and liquid flow does
not. We have not yet programmed the nozzle gas calculation since the demand for such a
program has not been as great as for the orifice gas calculation.

Due to streamlining of the device, liquid or gas flow through a venturi meter has a much
lower differential pressure compared to a nozzle or orifice. The low differential pressure
results in very little density change through the venturi - even for gases. Thus, the
expansibility factor is not present in the venturi equations. The equations are the same
for liquids and gases. Our venturi meter calculation is valid for liquids and gases.

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) 2000 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. April 21, 2000

Focus on Gas Flow Measurement using an Orifice

http://www.LMNOeng.com/Flow/OrificeGas.htm

Our newest calculation on the LMNO Engineering website is gas flow measurement in pipes
using an orifice. We have had an orifice calculation for liquid flow on the website for
several months, and have had requests for a gas flow calculation. The gas flow calculation
is based on equations in ISO (1991, 1998).

The orifice gas flow calculation has drop-down menus to solve for flowrate (mass and
volumetric), differential pressure, or orifice diameter. The user always enters upstream
pressure, gas temperature, and pipe diameter. There are also drop-down menus for various
gases - air, methane (natural gas), oxygen, and others. If one of the built-in gases is
selected, density is automatically computed using the ideal gas law. Viscosity and
isentropic exponent are also automatically set. The user can alternatively enter his/her
own values for density, viscosity, and isentropic exponent.

The gas calculation allows for gas expansion through the orifice. A parameter known as
expansibility - which depends on the diameter ratio, upstream pressure, pressure
differential, and isentropic exponent - is important in the gas flow calculation. The
presence of this parameter makes direct solution of flowrate, differential pressure, or
diameter impossible. All of the computations require an iterative type of solution. We
utilize a cubic solver method using double precision, which is very fast and highly
accurate.

To activate all of the features of this program for free, type in the password
"OrificeGas" on our homepage (http://www.LMNOeng.com)
using the case shown and without the quotation marks. The password is valid until April
27, 2000. The password enables all calculations on the website.

Thank you for your interest in the LMNO Engineering website.

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

References:

International Organization of Standards (ISO 5167-1). 1991. 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. Reference number: ISO
5167-1:1991(E).

International Organization of Standards (ISO 5167-1) Amendment 1. 1998. 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. Reference number:
ISO 5167-1:1991/Amd.1:1998(E).

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) 2000 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. March 28, 2000

Focus on Hydrology (Rainfall-Runoff)

http://www.LMNOeng.com/Hydrology/hydrology.htm

Recently, we received an inquiry regarding runoff due to low precipitation rainfalls from
someone using our Rainfall-Runoff Hydrology calculator. He noticed that runoff appeared to
increase as precipitation decreased for precipitations less than approximately 0.3 inch.
How can runoff increase as precipitation decreases?

The answer is that our calculation is based on the U.S. Soil Conservation Service
Technical Release 55 (TR-55) which states that its method for computing runoff is
recommended only for runoff greater than 0.5 inches. If the computed runoff is <0.5
inch, the message, "Most accurate if Q>0.5 inch" is displayed by our
calculation (Q is runoff depth).

The equations presented in TR-55 explain the behavior of the rainfall-runoff relationship.
The equations can also be found on our web page (web address indicated above):

Q=(P-Ia)^2/(P-Ia+s) Ia=0.2s s=1000/CN-10

where:

CN=runoff curve number (usually between 50 and 100, with pavement higher than grass).

Ia=Initial abstraction (inches). Ia is water loss before runoff begins; due to puddles,
leaves, evaporation, infiltration, etc.

P=precipitation (inches), Q=runoff depth (inches), s=potential maximum watershed water
retention after runoff begins (inches).

As an example, let CN=80. Then s=1000/80-10=2.5 and Ia=0.2(2.5)=0.5 inch. Then for various
values of P, the value of Q is computed:

P (inch) 10.0 5.0 1.0 0.5 0.2 0.1 0.01

Q (inch) 7.5 2.9 0.08 0.0 0.04 0.076 0.076

Q decreases with P until P=Ia, then Q increases even though P continues to decrease. The
TR-55 method was not developed for such low Q's and is not accurate if Q<0.5 inch.

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) 2000 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. March 8, 2000

Focus on Groundwater Flow Direction and Gradient

http://www.LMNOeng.com/Groundwater/gradient.htm

The newest addition to the LMNO Engineering website is a calculation for determining
groundwater flow direction and hydraulic (i.e. head) gradient in the direction of flow.
One enters at least three water table elevation measurements made at various x,y
locations. The calculation computes the flow direction and hydraulic gradient. The aquifer
can be confined or unconfined.

If the aquifer soil type is known, hydraulic conductivity can be entered and the flowrate
per unit aquifer width will be computed. The calculation is limited to homogeneous
aquifers - that is aquifers whose soil type is uniform.

For those interested in contaminant migration, after computing the gradient, you can use
our contaminant transport calculators to determine chemical concentrations down-gradient
from a release.

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) 2000 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. February 22, 2000

Free Password for LMNO Engineering website

In appreciation of our newsletter subscribers, the password (PIN) for our website is
"LMNOeng". Enter it on our home page without the quotation marks, and in the
case shown. Be sure the "LMNO" is all capital letters and the "eng" is
lower case. This password is valid until Sunday, February 27, 2000.

Feel free to let others know about the password, which provides free access to all of our
calculations - pipe flow, open channel flow, hydrology, groundwater, weirs, orifices,
nozzles, venturis, flow from a tank, unit conversions and more. http://www.LMNOeng.com

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) 2000 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. February 5, 2000

Focus on Groundwater Contaminant Transport

http://www.LMNOeng.com/Groundwater/transportPulse.htm

A previous newsletter introduced our calculation for determining groundwater chemical
concentrations down-gradient from a step injection of a chemical in a one dimensional flow
field. On Feb. 2, we added an additional web page (address above) for computing chemical
concentrations in three dimensions due to a pulse (or slug) injection of a chemical.

The pulse injection calculation is useful if a known mass of chemical is suddenly released
into an aquifer at location x,y,z=0,0,0. The chemical concentration can be computed at any
x, y, z location down-gradient (or up-gradient) from the release. In addition to computing
concentration, the calculation can compute mass injected or distances.

For example, if the concentration is measured as 10 mg/liter at a certain x, y, and z
location and at a certain time since the spill, the calculation can compute the mass of
the spill. Or, to protect a down-gradient population, the calculation can compute the
distance x along the centerline of the plume (y=0, z=0) where a concentration of, for
example, 1 mg/liter will occur due to a 1000 kg spill at a certain time after the spill.

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) 2000 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. January 21, 2000

Focus on Groundwater

http://www.LMNOeng.com/Groundwater/transportStep.htm

Our newest addition to the LMNO Engineering website is a groundwater contaminant transport
calculation. This calculation computes chemical concentration down-gradient from a
chemical injection or spill. It can be used to predict chemical concentration in a field
scale aquifer as well as a laboratory scale column. The user inputs the chemical's
concentration in the aquifer at the location of the injection and the duration of
injection. Then, concentrations at desired times and distances down-gradient are computed.

The calculation simulates advection, dispersion, and retardation of the chemical. The
calculation has convenient drop-down menus for selecting soil type with built-in values
for bulk density, porosity (total and effective), and hydraulic conductivity. Drop-down
menus are also provided for various chemicals with built-in values of the organic carbon
partition coefficient. The web page shows the equations that we programmed and allows you
to see the functionality of the calculation without paying to register.

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) 2000 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.

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

7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890

LMNO@LMNOeng.com

Newsletter. January 6, 2000

Focus on Moody Diagram

The Moody diagram is used to determine the Darcy-Weisbach friction factor (f) in
pressurized pipe flow of liquids and gases. It is a graph used by all who have taken a
college course in fluid mechanics. To refresh your memory, f is used in the following
equation for head loss (Darcy-Weisbach equation):

h = f L V^{2} / (2gD)

where h is head loss due to pipe friction [L], L is pipe length [L], V is fluid velocity
[L/T], g is acceleration due to gravity [L/T^{2}], D is pipe diameter [L], f is
friction factor [unit-less].

The Moody diagram is divided into three sections: Laminar flow, Transition flow, and
Turbulent flow. The three sections are based on the value of the Reynolds number (Re),
where:

Re=VD/v

Re is Reynolds number, v (small v) is kinematic viscosity of the fluid [L^{2}/T].
V and D are same as above.

If Re < 2100, the flow is considered laminar.

If Re > 4000, the flow is considered turbulent.

If Re is between the two values, the flow is considered to be in transition. There
currently is no standard means of determining f in the transition range. If Re is in the
transition range, I usually recommend computing head loss using both the laminar and
turbulent methods, and use the f that gives you the most conservative results.

In the turbulent range, f is a function of e/D as well as Re. e is the surface roughness
of the pipe [L]. (Note that Reynolds number "Re" is not R times e. The symbol
for surface roughness, "e", is separate from the Reynolds number symbol.)

In the laminar range, f=64/Re. In the turbulent range, the Moody graph or a numerical
approximation to the graph must be used. The two commonly used equations to approximate
the Moody chart will be discussed in a future newsletter - they are the Colebrook equation
and Swamee/Jain equation. The Colebrook is more accurate, and we use it in Design of
Circular Liquid or Gas Pipes ( http://www.LMNOeng.com/DarcyWeisbach.htm
). The Swamee/Jain equation is used in our free calculation http://www.LMNOeng.com/moody.htm
. If you view the latter equation on our web page, note that "ln" stands for
natural logarithm.

Additional pipe flow newsletters can be found at http://www.LMNOeng.com/Newsletters/newsletters.htm
.

Thank you for your interest in the LMNO Engineering website.

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

References:

Munson, Young, and Okiishi. Fundamentals of Fluid Mechanics. Wiley Pubs. 1998. 3ed.
(Chapter 8).

Streeter and Wylie. Fluid Mechanics. McGraw-Hill Pubs. 1985. 8ed. (Chapter 5).

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) 2000 LMNO Engineering, Research, and Software, Ltd.

**© 2000-2017 LMNO Engineering, Research, and Software, Ltd. (All
Rights Reserved)**

LMNO Engineering, Research, and Software, Ltd.

7860 Angel Ridge Rd. Athens, Ohio USA (740) 592-1890

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