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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890
LMNO@LMNOeng.com

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:

(P1-P2)/S = H

where P1=upstream pressure [F/L2], P2=downstream pressure [F/L2],
S=weight density of fluid [F/L3], H=major loss (also called friction loss) [L].
Note that S=dg where d=fluid density [M/L3] and g=acceleration due to gravity [L/T2].

H is a function of velocity, pipe roughness, diameter, and length. It is commonly represented by the Darcy-Weisbach friction loss equation (http://www.LMNOeng.com/DarcyWeisbach.htm) or the Hazen-Williams friction loss equation (http://www.LMNOeng.com/HazenWilliamsDesign.htm). After computing (P1-P2)/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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890
LMNO@LMNOeng.com

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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890
LMNO@LMNOeng.com

Focus on Detention Storage to Attenuate Storm Discharge
(http://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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890
LMNO@LMNOeng.comLMNO@LMNOeng.com

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 V2)/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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA   (740) 592-1890
LMNO@LMNOeng.com

Focus on Open Channel Flow Measurement: Rectangular Thin Plate Weirs
http://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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA   (740) 592-1890
LMNO@LMNOeng.com

Focus on Open Channel Flow Measurement: V-Notch Weirs
http://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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA   (740) 592-1890
LMNO@LMNOeng.com

Focus on Flow Measurement - Orifice Flowmeters in Pipes
http://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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA   (740) 592-1890
LMNO@LMNOeng.com

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 (http://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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA   (740) 592-1890
LMNO@LMNOeng.com

Focus on Hydrology (http://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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA   (740) 592-1890
LMNO@LMNOeng.com

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).

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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA   (740) 592-1890
LMNO@LMNOeng.com

Focus on Flow Measurement - Orifice Flowmeters in Pipes
http://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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA   (740) 592-1890
LMNO@LMNOeng.com

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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA   (740) 592-1890
LMNO@LMNOeng.com

Focus on Circular Culverts (not under pressure)

Take a look at the equations in Design of Circular Culverts (http://www.LMNOeng.com/CircularCulvert.htm) or Geometry of Circular Culverts (http://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=d2 [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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA   (740) 592-1890
LMNO@LMNOeng.com

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/T2], 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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA   (740) 592-1890
LMNO@LMNOeng.com

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)

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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA   (740) 592-1890
LMNO@LMNOeng.com

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 (http://www.LMNOeng.com/fluids.htm). The greek letter v ("nu") is kinematic viscosity. It has generic units of [L2/T] where L means length and T means time. The British Gravitational (BG) units and SI (International System) units are ft2/s and m2/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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA   (740) 592-1890
LMNO@LMNOeng.com

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 (http://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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA   (740) 592-1890
LMNO@LMNOeng.com

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 (http://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=h1+h2. Let h1 be the depth of water above the orifice. Let h2=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=h1 as expected for a tank open to the atmosphere. Let's look at an example. If h1=3 ft. and P=5 psig (pounds per square inch, gage pressure), then h2 = (5 lb/in2)(144 in2/ft2)/(62.3 lb/ft2)=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 h1.

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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA   (740) 592-1890
LMNO@LMNOeng.com

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 (http://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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA   (740) 592-1890
LMNO@LMNOeng.com

Focus on Open Channel Flow

The Manning Equation (http://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 (http://www.LMNOeng.com/CircularCulvert.htm) and rectangular channels (http://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 http://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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA   (740) 592-1890
LMNO@LMNOeng.com

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 http://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)D2, which is incorrect for a non-circular cross-section. Even though the D is the hydraulic diameter, (pi/4)D2 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)D2 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)D2 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: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA   (740) 592-1890
LMNO@LMNOeng.com

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 Z1-Z2, 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.