2005
December 21, 2005.  Gradually Varied Flow and Rapidly Varied Flow
October 27, 2005.  Flow Calculations
August 2, 3005.  Drainage Basin Peak Discharge
May 2, 2005.  Closed Conduit Flow Measurement and Bernoulli equation
March 17, 2005.  Weymouth and Panhandle Equations for Compressible Gas Flow
January 8, 2005.  Open Channel Flow Measurement

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA +1(740) 592-1890
LMNO@LMNOeng.com

Gradually Varied Flow (GVF) and Rapidly Varied Flow (RVF)

GVF and RVF are terms used to classify open channel flows - such as flow in rivers, canals, and culverts. RVF occurs over short distances such as when water flows over a weir or dam, drops off the end of a pipe, or encounters an hydraulic jump. GVF occurs over long distances such as the water approaching a weir, dam, or drop-off; or following a sluice gate.

In long prismatic (constant cross-section geometry) channels, the water will attempt to reach the "normal depth". Normal depth is the water depth determined using Manning's equation (or Chezy's equation). How the water depth changes with distance as it approaches its normal depth is called a GVF profile. A GVF profile is a computation of water depth versus distance along the channel length. A GVF computation typically involves starting at a known depth (e.g. at a dam) and making successive computations upstream using the continuity equation and energy slope in Manning's equation (rather than using the channel bottom slope). It is a numerical computation and for best accuracy you want to use the smallest distance increments possible. If you have had a course in open channel flow, you might recall the different GVF profile types - such as M1, M2, M3, S1, S2, S3, etc.

RVF computations require the continuity equation and the energy equation (like Bernoulli equation but with losses) and/or momentum equation. To analyze an hydraulic jump, continuity and momentum are required. To analyze flow over a dam/weir, continuity and energy are used. Often, empirical methods are used to analyze flow over weirs.

You can find equations and calculations for GVF and RVF under the Open Channels/Culverts heading on our home page http://www.LMNOeng.com .

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://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) 2005 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, Ohio 45701 USA (740) 592-1890
LMNO@LMNOeng.com

What calculation should I use?

Need the flowrate through a pinhole in a leaky pipe? Try our Bernoulli calculator: http://www.LMNOeng.com/Flow/bernoulli.htm

Need to know if a pump is required to carry water through your pipe? Try our Darcy-Weisbach or Hazen-Williams calculations without pump curve. Solve for pump head. If a pump is required, pump head will be positive. http://www.LMNOeng.com/DarcyWeisbach.htm or http://www.LMNOeng.com/HazenWilliamsDesign.htm

Need to know if a blower is required to carry air through your pipe? Try our Darcy-Weisbach calculation without pump curve: http://www.LMNOeng.com/DarcyWeisbach.htm . Solve for pump head like above. Note that you can't use Hazen-Williams for air since Hazen-Williams is only valid for water.

Need to know the flowrate through a pipe with a pump already installed? Try Darcy-Weisbach with pump curve (any liquid or gas) or Hazen-Williams with pump curve (water only): http://www.LMNOeng.com/Pipes/DWpump.htm or http://www.LMNOeng.com/Pipes/HWpump.htm

Need to know pressure change in a pipe due to an expansion or contraction? Try our Bernoulli calculator: http://www.LMNOeng.com/Flow/bernoulli.htm

Need a Moody friction factor? Try our Moody friction factor calculation: http://www.LMNOeng.com/moody.htm

Need to determine velocity using a pitot tube? Try our Bernoulli calculation: http://www.LMNOeng.com/Flow/bernoulli.htm

Need to determine discharge over a dam but our rectangular weir calculation gives "parameter out of range" messages? Try our Bernoulli calculation - not as accurate but no limits on the variables: http://www.LMNOeng.com/Flow/bernoulli.htm

Need the flowrate through an orifice plate, but our orifice calculation gives you a "parameter out of range" message? Try our Bernoulli calculator - not as accurate but no limits on the variables: http://www.LMNOeng.com/Flow/bernoulli.htm

Need to know pond storage volume required to attenuate a flood? Try our Detention basin storage calculation: http://www.LMNOeng.com/Hydrology/storage.htm

Need to analyze a network of pipes? Try http://www.LMNOeng.com/Pipes/PipeNetwork.htm

Need to determine gas viscosity? Try http://www.LMNOeng.com/Flow/GasViscosity.htm

Need to determine the volume of a partially full tank? Try http://www.LMNOeng.com/Volume/CylConeSphere.htm

Need to determine runoff from a watershed? Try http://www.LMNOeng.com/Hydrology/hydrology.htm

Have another question? Send me an e-mail ( LMNO@LMNOeng.com ) or give me a call (USA: 740/592-1890).

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

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) 2005 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, Ohio 45701 USA (740) 592-1890
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.

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

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://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) 2005 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, Ohio 45701 USA (740) 592-1890
LMNO@LMNOeng.com

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,
Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
http://www.LMNOeng.com  LMNO@LMNOeng.com

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) 2005 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

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

Three equations are often used for modeling the flow of natural gas. They are the Weymouth, Panhandle A, and Panhandle B equations. These three equations are not just for natural gas, however. They are valid for most other compressible gases as well. Our calculation page 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 ( http://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.
http://www.LMNOeng.com  LMNO@LMNOeng.com

Reference:
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) 2005 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, Ohio 45701 USA (740) 592-1890
LMNO@LMNOeng.com

Parshall Flume - Submerged and Free Flow
http://www.LMNOeng.com/Flumes/parshall.htm

LMNO Engineering's Parshall flume calculation computes discharge and rating curves for free flowing or submerged Parshall flumes. A free flowing flume can be identified by the drop in water depth at the flume throat. In submerged flow, the downstream water backs up into the throat swallowing the drop - making the drop difficult or impossible to identify. Analysis of submerged flow requires two head measurements - one in the approach channel and one in the throat; whereas, free flow requires only the upstream head measurement. Our Parshall flume calculation is based on the ISO 9826 (1992) standard.

Graphs of discharge versus head and discharge versus submergence ratio can be prepared on the web page. You can see that increasing the submergence ratio causes the discharge to decrease for a constant approach head. (Submergence ratio is defined as throat head divided by approach head.) The Parshall flume equations and methodology are described on the web page.

Our other flume calculation ( http://www.LMNOeng.com/Flumes/flumes.htm ) analyzes free flowing trapezoidal, rectangular, U-shape, and Parshall flumes. Both parshall.htm and flumes.htm use identical equations for free flowing Parshall flumes.

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

Reference:
International Organization of Standards (ISO 9826). 1992. Measurement of liquid flow in open channels - Parshall and SANIIRI flumes. Reference number: ISO 9826:1992(E).