2003
December 4, 2003.  Culvert Design using Inlet and Outlet Control
October 9, 2003.  Pipe Network Example
July 29, 2003.  Energy and Hydraulic Grade Lines
June 23, 2003.  Water Hammer (hydraulic transient)
May 21, 2003.  Time of Concentration for Watersheds
May 17, 2003.  Drainage Basin Peak Discharge
February 13, 2003.  Weymouth and Panhandle Equations for Compressible Gas Flow (New)
February 3, 2003.  New - Gas Viscosity Calculator
January 6, 2003.  Special Offer

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: https://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA (740) 707-2614
LMNO@LMNOeng.com

Culvert Design using Inlet and Outlet Control
https://www.LMNOeng.com/Pipes/hds.htm

Culverts have been utilized for thousands of years as a means to transmit water under walkways and roads. Too often, culverts are selected without sufficient thought of how much water needs to be convey under extreme conditions. If a culvert cannot convey all of the incoming water, then the water will flow over or around the pipe - or simply back up behind the culvert creating a pond or reservoir. If any of these conditions are unacceptable, then the proper culvert diameter and number of culverts must be selected prior to installation in order to convey all of the anticipated water through the pipe(s).

Discharge through a culvert is controlled by either inlet or outlet conditions. Inlet control means that flow through the culvert is limited by culvert entrance characteristics. Outlet control means that flow through the culvert is limited by friction between the flowing water and the culvert barrel. The term "outlet control" is a bit of a misnomer because friction along the entire length of the culvert is as important as the actual outlet condition (the tailwater depth). Inlet control most often occurs for short, smooth, or greatly downward sloping culverts. Outlet control governs for long, rough, or slightly sloping culverts. The type of control also depends on the flowrate. For a given culvert installation, inlet control may govern for a certain range of flows while outlet control may govern for other flowrates. If the flowrate is large enough, water could go over the road (or dam). In this case, our calculation automatically computes the amount of water going over the road and through each culvert, as well as the headwater depth.

Our culvert design calculation aids the designer in selecting the number of culverts and culvert diameter. It also plots headwater depth vs. discharge so that the designer can view culvert performanace over a wide range of flows. Our calculation is primarily based on the methodology presented in Hydraulic Design of Highway Culverts by Normann (1985) and published by the USA Department of Transportation's Federal Highway Administration.

Please see https://www.LMNOeng.com/Pipes/hds.htm to run the calculation and to see equations, diagrams, and additional description.

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
https://www.LMNOeng.com

Reference:
Normann, J. M. 1985. Hydraulic design of highway culverts. HDS-5 (Hydraulic Design Series 5). FHWA-IP-85-15. NTIS publication PB86196961. Obtainable at http://www.ntis.gov.

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(c) 2003 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: https://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614
LMNO@LMNOeng.com

Pipe Network Example
https://www.LMNOeng.com/Pipes/PipeNetwork.htm

I will present an example of how to determine the height of a city water tower using our Pipe Network calculation. Fluid: water at 20C. Pipe material: ductile iron (cast iron). Flow in gpd (gallons (US)/day), Elevations in ft, Diameters in inch, Pressure in psi, Head loss in psi, Lengths in ft, Z+P/S in ft. The water tower will be at node D.

In this example, the water tower is placed on a hill. The hill elevation is 50 ft. above all of the other nodes. All other nodes have the same elevation. All pipes are 10 inch inside diameter and 1000 ft. long. Each outfow node represents a collection of businesses or houses. For simplicity, let's say the required flows out of nodes A-C and E-I is 500,000 gpd each and the pressure requirement is 100 psi at each node. Therefore, set the pressure at the furthest node from the water tower to 100 psi to guarantee that all nodes will have at least 100 psi pressure. The node furthest from the water tower will be C or I (both are the same distance from node D since all pipes have the same length). I'll use node I.

Summary of inputs: Select "P known at node I". Enter Q node for nodes A-C and E-I as -5e5 gpd (be sure to use the negative sign since these are withdrawals). Enter Q node for node D as 4e6 gpd (this number is positive since it is the inflow to the system. I got 4e6 from 5e5 x 8 nodes). Enter the elevation of node D as 50 ft and all other node elevations as 0.0 ft. Enter the pressure at node I as 100 psi. Enter the diameter of each pipe as 10 inches and the length of each pipe as 1000 ft.

After making the proper data entries, click the "Calculate" button and look at the results. All node pressures A-C and E-I are at least 100 psi as required. Look at the node D results: the water tower required height is 238.71964 ft - 50 ft = 189 ft. (rounding to the nearest ft). The pressure of 81.7 psi is at the base of the tank (at an elevation of 50 ft). The pipe "H,V,Re pipe" fields are scrollable with your arrow keys, so you can see the head loss, velocity, and Reynolds number for each pipe. You can see the flowrate in each pipe and the direction of flow from the arrows. You might try reducing the diameters for pipes 5 and 10 to save money since they don't carry much flow.

A copy of this example is viewable at https://www.LMNOeng.com/Pipes/example3(4).htm. Note that the "H,V,Re pipe" field is not scrollable in the gif file.

I hope this example has been helpful,
Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
https://www.LMNOeng.com

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) 2003 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: https://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614
LMNO@LMNOeng.com

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.

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

Thank you for your interest in the LMNO Engineering website https://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) 2003 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: https://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614
LMNO@LMNOeng.com

Water Hammer (hydraulic transient)
https://www.LMNOeng.com/WaterHammer/WaterHammer.htm

Water hammer (also known as hydraulic transient) 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.

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.

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
https://www.LMNOeng.com  LMNO@LMNOeng.com

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) 2003 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: https://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614
LMNO@LMNOeng.com

Time of Concentration for Watersheds
https://www.LMNOeng.com/Hydrology/TimeConc.htm

Time of concentration is a fundamental watershed parameter. It is used to compute the peak discharge for a watershed. The peak discharge is a function of the rainfall intensity, which is based on the time of concentration.

Time of concentration is defined as the longest time required for a particle to travel from the watershed divide to the watershed outlet. Each of the three equations used in our time of concentration calculation require inputs for the longest watercourse length in the watershed (L), the average slope of that watercourse (S), and a coefficient representing the type of groundcover. Usually L and S can be obtained from topographic maps. The coefficient is determined from photographs of the watershed or field reconnaissance. Our calculation computes the time of concentration and average velocity in the longest watercourse. A variety of units may be selected.

Our calculation uses the FAA, Kirpich, and Kerby equations. The FAA (U.S. Federal Aviation Administration) equation is the most commonly used of the three because it uses the widely recognized Rational Coefficient to describe watershed ground cover. The Kirpich equation, developed in 1940, is the oldest of the three equations and is probably the most widely recognized, but no longer the most commonly used. The Kerby equation is the least common of the three equations and has the most limitations.

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
https://www.LMNOeng.com  LMNO@LMNOeng.com

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) 2003 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: https://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614
LMNO@LMNOeng.com

Drainage Basin Peak Discharge

Today's topic is runoff during a storm. In order to size culverts, pipes, and channels to convey runoff from a watershed, a design discharge (i.e. flowrate; units typically are gpm, cfs, or cms) must be determined.

Two common methods for determining the peak discharge from a storm are the SCS TR-55 Peak Discharge Method and the Rational Method. The Rational Method is usually used for sizing storm sewer inlets and culverts in urban areas, where drainage areas are small and times of concentration are short. The SCS method is for somewhat larger watersheds with times of concentration between 6 minutes and 10 hours.

Both methods require knowing the storm intensity (typical units are inch/hour or cm/hour). The storm intensity is a function of the return period and storm duration. The return period is usually specified by a local government and depends on the impact of under-designing conveyances. Return periods may be 10-yr, 25-yr, 50-yr, or even 100-yr. The larger the return period, the larger the storm and the more conservative the design.

The SCS method uses a 24-hr duration storm. For the Rational Method, the storm duration is equivalent to the time of concentration. The time of concentration is the time required for the most distant (time-wise) water particle in the watershed to reach the mouth of the watershed.

In addition to the storm intensity, the Rational and SCS methods require knowing the drainage area and runoff coefficient. The SCS method has additional inputs depending on the degree of detail required.

https://www.LMNOeng.com/Hydrology/rational.htm   (Rational Method)
https://www.LMNOeng.com/Hydrology/hydrology.htm   (SCS Method)

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
https://www.LMNOeng.com  LMNO@LMNOeng.com

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) 2003 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: https://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614
LMNO@LMNOeng.com

Weymouth and Panhandle Equations for Compressible Gas Flow
https://www.LMNOeng.com/Flow/weymouth.htm

In our November 2, 2002, newsletter I mentioned that we would soon have some natural gas calculations. We now have the Weymouth, Panhandle A, and Panhandle B equations and calculators on-line.

These three equations are not just for natural gas, however. They are valid for most other compressible gases as well. Our calculation includes a drop-down menu for you to choose which of the three equations to use and the gas (air, natural gas, nitrogen, oxygen, butane, carbon dioxide, propane). You may select the last option in the gas drop-down menu, which allows you to enter the specific gravity for an unlisted gas. The drop-down menu also allows you to select which variable to compute (flowrate, pipe diameter, length, or pressure) as well as a variety of units. Actual and standard volumetric flowrates are shown.

Background
The Weymouth, Panhandle A, and Panhandle B equations were developed to simulate compressible gas flow in long pipelines. The Weymouth is the oldest and most common of the three. It was developed in 1912. The Panhandle A was developed in the 1940s and Panhandle B in 1956 (GPSA, 1998). The equations were developed from the fundamental energy equation for compressible flow, but each has a special representation of the friction factor to allow the equations to be solved analytically.

The Weymouth equation is the most common of the three - probably because it has been around the longest. The equations were developed for turbulent flow in long pipelines. For low flows, low pressures, or short pipes, they may not be applicable. If the pressure drop in a pipeline is less than 40% of upstream gage pressure, then our Darcy-Weisbach incompressible flow calculation ( https://www.LMNOeng.com/DarcyWeisbach.htm ) may be more accurate than the Weymouth or Panhandles for a short pipe or low flow. The Darcy-Weisbach incompressible method is valid for any flowrate, diameter, and pipe length, but does not account for gas compressibility.

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
https://www.LMNOeng.com  LMNO@LMNOeng.com

Reference:
Crane Co. Flow of fluids through valves, fittings, and pipe. Technical Paper 410 (TP 410). 1988.

GPSA (Gas Processors Suppliers Association). Engineering Data Book. 11ed. 1998.

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) 2003 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: https://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614
LMNO@LMNOeng.com

New - Gas Viscosity Calculator
https://www.LMNOeng.com/Flow/GasViscosity.htm

We have recently completed a relatively simple calculator to provide gas viscosity as a function of temperature. Dynamic viscosity is
primarily a function of temperature, rather than pressure, for pressures up to 500 psi (34.5 bar) (Crane, 1988).

Our gas viscosity calculator is based on the methodology in Crane (1988) and the CRC Handbook of Chemistry and Physics. The
viscosity of many gases can be computed by the Sutherland formula shown on the web page. For natural gases with various specific
gravities, the Sutherland formula does not apply. In this case, we have taken data points from graphs in very small intervals and input
them into our calculation. Then, the calculation interpolates linearly between the points.

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
https://www.LMNOeng.com  LMNO@LMNOeng.com

References:
Chemical Rubber Company (CRC). 1984. CRC Handbook of Chemistry and Physics. Weast, Robert C., editor. 65th edition. CRC
Press, Inc. Boca Raton, Florida. USA.

Crane Company. 1988. Flow of fluids through valves, fittings, and pipe. Technical Paper No. 410 (TP 410).

You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating

(c) 2003 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: https://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 707-2614
LMNO@LMNOeng.com

Special Offer

We are offering a New Year special. Purchase a 7-day subscription for \$30, then e-mail the password to me. I will send you a new password good for 6 months at no additional charge.

This special offer will expire on January 15, 2003.
Additional Note: If you are reading this newsletter on-line, the offer is valid until March 15, 2003.

How it works:
The 7-day password enables all calculations on our site for 7 days beginning when you first type the 7-day password into our home page.

The 6-month password enables all calculations on our site for 6 months beginning when you first type the 6-month password into our home page.

Therefore, you can purchase the password now, but type it in later (days, weeks, months, years from now - it doesn't matter). The expiration date of a password is based on when you first enter it into our home page. The expiration date is not based on when you purchase the password.

Passwords can be purchased at https://www.LMNOeng.com/register.htm . Passwords are also known as PIN numbers.

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
https://www.LMNOeng.com  LMNO@LMNOeng.com

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) 2003 LMNO Engineering, Research, and Software, Ltd.