2004
October 27, 2004.  Pressured Non-Circular Ducts/Conduits
September 15, 2004.  Gradually Varied Flow
July 14, 2004.  End Depth Method for Flow Measurement in Open Channels
May 18, 2004.  Detention Storage to Attenuate Storm Discharge
April 1, 2004.  Force due to Pipe Bend - new calculation
March 3, 2004.  Hydraulic Jump
January 21, 2004.  Open Channel Flow Measurement

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

Pressurized Non-Circular Ducts/Conduits

Our "Non-Circular to Circular Pipe Conversions" at http://www.LMNOeng.com/PipeDuct.htm 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 non-circular to circular 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 circular design calculation page and copy it to the non-circular to circular calculation page so that the velocity is multiplied by the actual duct area. This will give the correct flowrate. The flowrate output in the circular pipe 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.

Conversely, if you use "Design of Circular Water Pipes" to determine a pipe diameter based on a required velocity, the non-circular to circular 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.

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) 2004 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

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. I'll leave discussion of these to another newsletter!

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.

Additional discussion can be found at http://www.LMNOeng.com/Channels/gvf.htm.

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) 2004 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 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.

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) 2004 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

Detention Storage to Attenuate Storm Discharge
http://www.LMNOeng.com/Hydrology/storage.htm

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

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) 2004 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

Force due to Pipe Bend - new calculation
http://www.LMNOeng.com/Force/ForceBend.htm

We added a new calculation to our website on March 12. It computes the reaction force required to hold a pipe bend in place as a fluid flows around a horizontal bend in a pipe. In order to properly size thrust blocks, hangars, or other devices to hold a pipe in place, the momentum equation is used to compute the necessary resistive force to hold the pipe stationary.

Forces in a pipe bend in the horizontal plane are caused by the fluid's momentum and pressure. If the pipe undergoes a bend in the vertical plane, where the entrance to the bend is above the exit (or vice-versa), then the weight of the liquid and pipe material within the bend will contribute to the force. Since computing the volume of fluid and pipe material within a bend requires considerably more input, we kept our calculation relatively simple by keeping it in the horizontal plane.

The calculation displays the reaction force in two ways:
1. The x and y components of the reaction force are shown, and
2. The resultant force and its direction are shown.

Equations and flow diagrams can be seen on the web page. The calculation has a demonstration mode so that you can enter different variables and see the results.

Thank you for your interest in the LMNO Engineering website,
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) 2004 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

Hydraulic Jump - new calculation
http://www.LMNOeng.com/Channels/HydraulicJump.htm

We wrote a new calculation for our website. It is a hydraulic jump calculator for open channel flow in a rectangular channel. The user enters the channel width, discharge, and upstream depth. The calculator computes downstream depth, jump length, head loss over the jump, Froude numbers, and flow velocities.

A hydraulic jump can only occur when the upstream flow is supercritical (F>1). In addition, to have a jump there must be a flow impediment downstream. The downstream impediment could be a weir, a bridge abutment, a dam, or simply channel friction. Water depth increases over a hydraulic jump and energy is dissipated as turbulence.

Often, engineers will purposely install impediments in channels in order to force jumps to occur. Mixing of coagulant chemicals in water treatment plants is often aided by hydraulic jumps. Concrete blocks may be installed in a channel downstream of a spillway in order to force a jump to occur thereby reducing the velocity and energy of the water. Flow will go from supercritical (F>1) to subcritical (F<1) over a jump.

Please enter the free PIN: jump

Thank you for your interest in the LMNO Engineering website,
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) 2004 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

Open channel flow measurement

We offer calculations for three commonly used methods for open channel flow measurement - weirs, flumes, and end depth. The end depth method is the simplest because a structure does not need to be built - water drops freely from the downstream end of a culvert or channel. All that is needed are the dimensions of the culvert or channel and the water depth. Freely discharging culverts are widely used as discharge structures, and a picture of one is shown at http://www.LMNOeng.com/Waterfall/CulvertDischarge.htm.

Weirs are used for flow measurement when large head losses are acceptable and free discharge can be accommodated. Weirs are relatively inexpensive to construct, install, and operate. However, weirs will back up the flow since they are obstructions across the channel width and cause low velocities upstream of the weir. Sediment will build up behind the weir. A simple triangular (or V-notch) weir is shown at http://www.LMNOeng.com/Weirs/vweir.htm.

Flumes are more expensive than weirs but have the advantage of much less head loss. They are flow-through devices that do not cause the water to back up like weirs do. There are various types of flumes which are designed to allow varying ranges of discharge through them while minimizing sediment build-up and head loss. A flume photograph can be found at http://www.LMNOeng.com/Flumes/flumes.htm.

Thank you for your interest in the LMNO Engineering website,
Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://www.LMNOeng.com