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

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

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

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

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

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.

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:
TH1 + Pump Head = TH2 + Losses, so that TH2 can be computed as:
TH2 = TH1 + Pump Head - Losses

HH2 = TH2 - Velocity Head at 2 = TH1 + Pump Head - Losses - Velocity Head at 2
where location 1 is upstream of location 2.

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

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

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

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 m3/s, ft3/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

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 Lbf represent pounds force and Lbm represent pounds mass. If you only use the metric system, then you never need to worry about Lbf and Lbm. However, for those who work with English units, Lbf and Lbm are often troublesome.

Lbm is an inconsistent unit. It is not consistent with British Gravitational (BG) Units or US Customary (USC) Units. BG (and USC) units use Lbf, slugs, feet, and seconds. Slug is the unit of mass. 1 Lbf = 1 slug-ft/s2. The BG unit for mass density is slug/ft3. Many engineers use Lbm/ft3 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/s2 and h=10 ft. Using the BG system, d=1.94 slug/ft3 for water at 60F.
Therefore, P=(1.94 slug/ft3)(32.174 ft/s2)(10 ft)(1 Lbf-s2/slug-ft)=624 Lbf/ft2.

For those of you who use Lbm a lot (the EE system), you might be tempted to use d=62.4 Lbm/ft3 at 60F. Then
P=(62.4 Lbm/ft3)(32.174 ft/s2)(10 ft)=20,077 Lbm/ft-s2, which is not a pressure unit and is an incorrect use of units.

You can still use the 62.4 Lbm/ft3, but it must be used in a different way.
Note that 32.174 Lbm = 1 slug. Therefore, d=(62.4 Lbm/ft3)/(32.174 Lbm/slug)=1.94 slug/ft3.
Therefore, P=(1.94 slug/ft3)(32.174 ft/s2)(10 ft)(1 Lbf-s2/slug-ft)=624 Lbf/ft2, 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 Lbf = 1 Lbm numerically, though Lbf is a force unit and Lbm is a mass unit. You can think of 62.4 Lbm/ft3 as equivalent to 62.4 Lbf/ft3. 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/ft3)(10 ft)=624 Lbf/ft3, 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

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

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)

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

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

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

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

Focus on Groundwater Flow Direction and Gradient

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

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

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

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

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 V2 / (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/T2], 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 [L2/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.

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.