Newsletters 2020-2024: LMNO Engineering, Research, and Software - hydrology, culverts, water hammer, gas leak, weirs

Newsletters
2020 - 2024

LMNO Engineering, Research, and Software, Ltd.

Index to all Newsletters
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LMNO Engineering home page email: LMNO@LMNOeng.com
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2020
January 2, 2020. Focus on Hydrology - Impact of Culvert Replacement
January 22, 2020. Open Channel Uniform and Non-Uniform Flow
February 19, 2020. Gas Leak Rate Calculator - New
May 6, 2020. Calculators
August 13, 2020. Gradually Varied Flow

2021
March 11, 2021. Water Hammer
October 18, 2021. Parshall Flume for Stream Flow Measurement

2022
February 8, 2022. Gas Flow Conversions
March 2, 2022. Open Channel Flow Modeling
June 14, 2022. Culvert Design using Inlet and Outlet Control
November 10, 2022. Partially Full Inclined Cylinder Volume Calculation

2023
January 19, 2023. Choked Flow of Gas from a Tank through a Pipe
August 24, 2023. Riprap Rock Sizing Calculator
October 17, 2023. Liquid Flow in Pipes
November 16, 2023. Liquid Flow in Pipes with a Pump Curve

2024
February 6, 2024. Weirs for Open Channel Flow Measurement
March 26, 2024. Pump Inlet Conditions
July 9, 2024. Gradually Varied Flow - more discussion

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

Newsletter. January 2, 2020.

Focus on Hydrology - Impact of Culvert Replacement

We recently completed a culvert design consulting project. Culvert design is a mature field, so it would seem that most of the nuances have been worked out. However, sometimes the impacts of culvert replacement are overlooked. A culvert may be replaced due to its having been partially crushed or having deteriorated so that it no longer properly conveys the intended design flow at the original design upstream head (water depth). It is tempting to simply replace the culvert with the same or larger size. While this is usually the strategy, it can have unintended downstream consequences.

Replacing a culvert with the same or larger diameter, and clearing brush/debris, results in less flow resistance - which is a desirable consequence. However, the failed culvert may have provided stormwater detention upstream of the culvert. Upon replacement, there is less flow resistance resulting in less upstream stormwater detention and an increased risk of downstream flooding.

Please let me know if questions. Thank you for your interest in the LMNO Engineering newsletter,

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

Culvert design calculator: https://www.LMNOeng.com/Pipes/hds.php

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Open Channel Uniform and Non-Uniform Flow

The empirical Manning equation is the most commonly used equation for open channel flows. In open channel flow, the water surface is open to the atmosphere. For instance, open channel flow can be in a partially full pipe, in a natural stream or river, or in a manmade channel. The Manning equation is of the form:

Q = A k R^2/3 S^1/2 / n

where: Q = Flow rate (m³/s or ft³/s). A = Cross-sectional flow area (m² or ft²). k = Unit conversion factor = 1 for SI units or 1.49 for English units. R = Hydraulic Radius (m or ft) = A/P, where P = Wetted perimeter (m or ft). S = Energy slope = Change in water surface elevation per unit length of channel (m/m or ft/ft). n = Manning roughness factor.

If the channel or pipe that water is flowing through is long with unchanging dimensions (a "prismatic" channel), then the water depth will be nearly constant along the channel's length. This situation is called uniform flow; the water surface is modeled as being parallel to the channel bottom. In this case, the slope of the channel can be used as the energy slope S. However, if the channel is not prismatic or the water depth changes with distance (near a channel drop-off for instance), then the energy slope S is the slope of the water surface, rather than the slope of the channel.

In many instances, we know the flow rate in the channel and need to determine the water depth. In this case, the Manning equation is solved for water depth numerically since S, A, and P (thus R) are functions of the water depth. If flow is uniform, then water depth is constant along the entire channel, so the Manning equation only needs to be solved numerically once for depth. If the water depth varies along the channel length (non-uniform flow), then the Manning equation is solved numerically for water depth, not just once, but over and over at small distance increments successively moving upstream or downstream along the channel.

More information can be found on our web pages: Uniform flow in pipe: https://www.LMNOeng.com/CircularCulvert.php
Uniform flow in trapezoidal channel: https://www.LMNOeng.com/Channels/trapezoid.php
Non-uniform flow in trapezoidal channel: https://www.LMNOeng.com/Channels/gvf.php (has demo mode and graph; note that non-uniform flow is also called gradually varied flow)

Please let me know if questions. Thank you for your interest in the LMNO Engineering newsletter,

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

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"Discontinue Newsletter" to LMNO@LMNOeng.com.

New calculator - Gas Leak Rate
https://www.LMNOeng.com/Gas/GasLeakRate.php

Gas can intentionally or unintentionally be vented from a tank or pipe to the surrounding air. The gas venting may occur through an orifice, crack, or other opening. Depending on the type of gas, temperature, and pressures, the gas flow may either be choked or subsonic as it exits through the hole. If flow is choked, the gas exits the tank at sonic velocity (Mach number of 1). If flow is subsonic, then the discharge Mach number is less than 1. As gas leaks through the crack, temperature drops. If the gas contains water vapor, then there is a possibility of freezing of entrained liquid.

In the calculator, you can select the type of gas or enter the specific gravity (or molecular weight) and specific heat ratio. Other inputs include tank pressure, tank temperature, ambient pressure, and hole size. The calculation is for steady state conditions. The computed values include mass flow rate, velocity through the hole, Mach number, and temperature.

Please let me know if questions. Thank you for your interest in the LMNO Engineering newsletter,

Ken Edwards, Ph.D., P.E. (Owner/Engineer)
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.

Calculators

As you know, we offer calculators for pressurized pipe flow, open channel flow, hydrology, and groundwater. Our list of calculators can be found at https://www.LMNOeng.com

Our pressurized pipe flow calculations are for liquid or gas flow. For compressible gases, we solve the Weymouth equation for pipelines and also compute leak rates and consider choked flow. We also offer a pipe network calculation for liquids, water hammer calculations, and pressure relief valve sizing. In addition, we have design calculators for orifice, nozzle, and venturi flow meters. We also have a fire hydrant residual pressure calculation, time to empty a liquid tank, and a general Bernoulli equation calculator.

For open channel flow, we have calculators for circular culverts and trapezoidal channel analysis. In addition, we offer a calculator for inlet and outlet control for culvert sizing. A gradually varied flow calculator computes water depth in a trapezoidal channel for subcritical and supercritical flows. Our inverted siphon calculator sizes pipes for going under rivers, highways, or other obstacles. We also have flow measurement calculators for flumes and weirs.

Regarding hydrology, we have calculators for rainfall-runoff, time of concentration, and storage basin sizing.

Our groundwater calculators compute flow through a permeameter, groundwater flow direction based on well head readings, and solve contaminant transport equations.

We also have calculators to determine the volume of a partially full inclined cylinder, riprap sizing, drag force, gas flow conversions between standard and actual, ideal gas, and gas viscosity as a function of temperature.

We also offer consulting services. If you have any questions, please let me know. Thank you for your interest in the LMNO Engineering newsletter,

Ken Edwards, Ph.D., P.E. (Owner/Engineer)
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
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Gradually Varied Flow Calculator: https://www.LMNOeng.com/Channels/gvf.php

My newsletter on May 6, 2020, described many of our flow calculators. Today's newsletter will focus on our gradually varied flow (gvf) calculator.

Unlike uniform flow in an open channel, gradually varied flow equations predict water depth as a function of longitudinal distance upstream or downstream from a location with a known depth. The computation of the water depth allows one to determine if channel over-topping will occur. Further, since water velocity varies with depth, an estimation of scouring can be determined by using the gvf computation of velocity along the channel.

Our calculator has a nice graphical feature where one can view plots of water depth, water surface elevation, velocity, top width, and Froude number with distance along the channel.

The calculator has a demonstration mode which allows one to see the functionality and graphing capabilities.

If you have any questions, please let me know. Thank you for your interest in the LMNO Engineering newsletter,

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

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"Discontinue Newsletter" to LMNO@LMNOeng.com.

Instantaneous Valve Closure - Water Hammer
https://www.LMNOeng.com/WaterHammer/impulse.php

Let's look at an example:
Water flows steadily out of a reservoir through an 8-inch Schedule 40 horizontal steel pipe (inside diameter 7.981 inch, wall thickness 0.322 inch) at 4 ft/s. The pipe is 100 ft long and has a valve at the end. The valve suddenly closes. How much will the pipeline pressure increase due to the valve closure?

Answer: The rise in pressure is predicted to be 233 psi due to the instantaneous valve closure.

Note: 7.981 inch= 20.27 cm, 0.322 inch= 0.818 cm, 4 ft/s= 1.22 m/s, 233 psi= 16.1 bar

How fast is an instantaneous valve closure? To be considered an instantaneous closure, the valve would need to close faster than the time required for a pressure wave to travel two pipeline lengths. When a valve closes at the downstream end of a pipeline, a pressure wave propagates upstream, bounces off the upstream reservoir/pipe connection, and propagates back down to the valve. Thus, the pressure wave travels two pipeline lengths to get back down to the closed valve. The valve must close quicker than this time period to be considered instantly closed.

In our example, the wave speed (celerity) is 4332 ft/s. Thus:

Instant valve closure if closure time < 2L/c with L=pipe length, c=celerity
Therefore: 2L/c=2(100 ft)/(4332 ft/s)=0.046 seconds

In this example, a closure time less than 0.046 seconds is considered instantaneous. If the valve takes longer than 0.046 seconds to close, the pressure rise would be less than 233 psi.

The type of liquid, velocity, pipe material, pipe diameter, and pipe wall thickness affect the magnitude of the pressure surge. Additionally, the pipe length affects the definition of instantaneous valve closure time.

We also offer a more complex water hammer calculation where you can enter the valve closure or opening time at https://www.LMNOeng.com/WaterHammer/WaterHammer

Thank you for your interest in the LMNO Engineering newsletter,

Ken Edwards, Ph.D., P.E. (Owner/Engineer)
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.

Parshall Flume for Stream Flow Measurement
https://www.LMNOeng.com/Flumes/parshall.php

There are many methods for measuring flow rate in streams, generally called open channel flow measurement. One method for flow measurement is the use of flumes. Flumes are built to standardized dimensions. One particular type of flume is the Parshall flume.

LMNO Engineering has a calculation for computing 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 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 (https://www.LMNOeng.com/Flumes/flumes.php) analyzes free flowing trapezoidal, rectangular, U-shape, and Parshall flumes. Both parshall.php and flumes.php use identical equations for free flowing Parshall flumes.

Thank you for your interest in the LMNO Engineering newsletter,

Ken Edwards, Ph.D., P.E. (Owner/Engineer)
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.

Gas flow conversions
https://www.LMNOeng.com/Flow/GasFlow.php

There is often confusion about how gas flowrates are stated. We have a calculator to aid in unit conversions for gas flow. Some gas flows are expressed in mass units, like kg/s or lb/day. Sometimes, flow units are acfm, scfm, or Nm3/s, to name a few.

Mass flowrate is straightforward. It is the amount of mass flowing per unit time. Volumetric flowrates, however, are either expressed as flow at "actual conditions" or flow at "standard (or normal) conditions". Units for flow at actual flowing conditions often have the letter "a" in front of the unit.

In contrast to flow at actual conditions, flows can be expressed at standard (or normal) conditions. English units usually are prefaced with the word "standard" or letter "s" while metric units are usually prefaced with the word "normal" indicated by the letter "N" (don't confuse with the Newton unit).

Standard (or normal) flows are the volume equivalent to actual flow if the actual flow were at standard temperature and pressure. For the same mass and temperature of gas, one cubic meter of a gas at 10 atmospheres of pressure occupies much more volume when its pressure is reduced to 1 atmosphere. Think of gas in a cylinder acted on by a piston.

Please see our web page https://www.LMNOeng.com/Flow/GasFlow.php for equations and further discussion of gas conversions.

Thank you for your interest in the LMNO Engineering newsletter,

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.

Open Channel Flow Modeling

Open channel flow modeling, also called river routing or river modeling, is usually used to determine water surface elevations along a river. The results help communities determine the potential for flooding.

In the U.S., the most common computer model for river routing is HEC-RAS. This stands for Hydrologic Engineering Center - River Analysis System. The model was developed by the U.S. Army Corps of Engineers. The model was originally called HEC-2. HEC-1 was the hydrologic model, now called HEC-HMS (Hydrologic Modeling System).

HEC-2, now HEC-RAS, progressed from one-dimensional steady state modeling to unsteady modeling to multiple dimensional modeling with GIS (Geographic Information System) capabilities.

The core of HEC-RAS has always been, and continues to be, conservation of mass, momentum, and energy. As from its original implementation, the Manning equation is at the heart of the model.

HEC-RAS modeling runs from the basic to the complex. For simpler modeling, LMNO Engineering offers calculations that use the Manning equation for uniform flow steady state design and analysis. We also offer a gradually varied flow calculator that allows the user to enter the upstream or downstream water depth. The program computes the water surface elevation along the channel.

HEC-RAS free download: https://www.hec.usace.army.mil/software/hec-ras/

Design of trapezoidal open channels: https://www.LMNOeng.com/Channels/trapezoid.php

Gradually varied flow (with graphing): https://www.LMNOeng.com/Channels/gvf.php

LMNO Engineering also offers consulting services in open channel flow modeling. Thank you for your interest in the LMNO Engineering newsletter,

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.

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

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 conveyed 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 performance over a wide range of flows.

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

Thank you for your interest in the LMNO Engineering newsletter,

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.

Partially Full Inclined Cylinder Volume Calculation
https://www.LMNOeng.com/Volume/InclinedCyl.php

Our inclined cylinder volume calculator computes the volume of liquid contained in a partially full inclined cylinder. It can be used for computing the liquid volume in a storage tank that is not horizontal. Or, for example, it can compute the volume of liquid in a pipeline that is sloped. The user enters the cylinder diameter, length, and angle from horizontal.

The calculation allows you to enter the liquid depth measurement several ways:

1. Vertical distance (i.e. perpendicular to liquid surface) from bottom of tank to liquid surface (i.e. wet depth).

2. Vertical distance from top of tank down to liquid surface (i.e. dry depth).

3. Distance from bottom of tank to liquid surface measured perpendicular to bottom of tank (i.e. parallel to the end caps).

4. Distance from top of tank to liquid surface measured perpendicular to top of tank. Since the cylinder is at an angle, the user must also indicate how far from the downhill edge of the tank the distance measurement is made.

The calculator also provides graphical and tabular results. It will produce a rating curve of volume versus measured distance. Charts and tables are produced by clicking on the "Click to Calculate" button and then clicking on the "Graph (opens in new tab)" or "Table (opens in new tab)" links.

A full description of the governing equations, inputs, and outputs are shown on the web page. If you are interested in the mass of liquid in the tank, just multiply the output volume by the liquid density.

The calculation has a demonstration mode for an angle of 15 degrees and tank diameter of 2 meters.

Thank you for your interest in the LMNO Engineering newsletter,

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.

Choked Flow of Gas from a Tank through a Pipe
https://www.LMNOeng.com/Gas/choke.php

Many gas flows will choke when they discharge to the atmosphere. Typically if tank pressure (or pipeline pressure, depending on pipeline length and diameter) is just a few atmospheres above pipe discharge pressure, flow will choke. If this condition is likely in your piping system, it is important to use a computation method that determines whether or not choked flow occurs. Otherwise, system flow rate will not be properly computed.

Choked flow has a Mach number of 1. That is, the gas velocity discharging from the pipe is sonic. Our choked flow calculation determines if a flow is choked. If so, it computes flow rate as well as pressures, velocities, Mach numbers, temperatures, and densities at the pipe entrance and pipe exit when the exit condition is choked. Inputs include tank pressure, tank temperature, pipe diameter, pipe length, type of gas, and outlet pressure. Our calculation assumes that flow is adiabatic (Fanno flow), no heat transfer. This is physically accomplished by pipe insulation.

If flow is not choked at the pipe exit, the program will indicate "Not choked." In this case a different method should be used to compute the flow rate.

Thank you for your interest in the LMNO Engineering newsletter,

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.

Riprap Rock Sizing Calculator
https://www.LMNOeng.com/Channels/riprap.php

Our riprap calculator uses the Isbash equation to size rocks (or stones) for river and stream channel stabilization. In the calculator, you enter the water velocity. The software computes the minimum rock size that will not get transported away. You also type in the rock specific gravity and an Isbash constant of 0.86 or 1.2. A constant of 0.86 should be used to determine the rock size to keep loose surface rocks from moving due to the water current. A constant of 1.2 can be used if the rock is in a pile with other rocks allowing them more resistance due to the group of rocks. Using an Isbash constant of 1.2 results in smaller rock size than using a value of 0.86.

The calculation can alternatively be solved for water velocity. In this case, you would enter the rock size.

Thank you for your interest in the LMNO Engineering newsletter,

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.

Liquid Flow in Pipes
https://www.LMNOeng.com/DarcyWeisbach.php

One of the first calculations we ever wrote for the LMNO Engineering Fluid Flow Calculations website back in 1999 can be found at https://www.LMNOeng.com/DarcyWeisbach.php

It remains one of our most popular calculations. The calculation is based on the steady state incompressible energy equation utilizing Darcy-Weisbach friction losses as well as minor losses, such as fittings and valves. The pipe flow calculation can compute flow rate, velocity, pipe diameter, elevation difference, pressure difference, pipe length, minor loss coefficient, and pump head (total dynamic head). The density and viscosity of a variety of liquids (and gases) are coded into the program, but you can alternatively select "User defined fluid" and enter the density and viscosity for fluids not listed. The program is valid for gas flow if the pressure differences are small enough that the gas can be modeled as incompressible.

Since boundary conditions affect the flow characteristics, our pipe flow calculator allows you to select whether your locations 1 and 2 are within pipes, at the surface of open reservoirs, or in pressurized mains (same as pressurized tank).

Thank you for your interest in the LMNO Engineering newsletter,

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.

Liquid Flow in Pipes with a Pump Curve
https://www.LMNOeng.com/Pipes/DWpump.php
https://www.LMNOeng.com/Pipes/HWpump.php

We have calculators for open channel flow, groundwater, volume of liquid in a horizontal or sloped tank, hydrology, drag force, riprap sizing, flow measurement in pipes and open channels, water hammer, liquid and gas leak rates, gas choked flow, liquid flow in a pipe, and gas flow in a pipe.

Last month, I discussed our most popular calculations which are for design and analysis of pipes to convey liquids and gases.

I have not written about pump curves for many years. If a pump is needed, it must be able to pump the desired flow against the system's head (i.e. pressure). We have calculators that allow you to enter system properties such as pipeline diameter, length, pipe material, elevation change, and minor losses for fittings; and pump characteristics such as maximum flow and maximum head. The calculator will compute the actual flow rate through the system, the total dynamic head, and the net positive suction head available.

https://www.LMNOeng.com/Pipes/DWpump.php uses the Darcy Weisbach friction loss method which is valid for nearly all liquids.

https://www.LMNOeng.com/Pipes/HWpump.php was developed for water supply systems and is only valid for water.

Thank you for your interest in the LMNO Engineering newsletter,

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.

Weirs for Open Channel Flow Measurement
https://www.LMNOeng.com/Weirs/vweir.php
https://www.LMNOeng.com/Weirs/cipoletti.php
https://www.LMNOeng.com/Weirs/RectangularWeir.php

Weirs are an inexpensive device used for flow rate measurement in open channels such as streams. Images can be seen by clicking on the above links. Weirs are plates (or thicker-walled concrete with a sharp edge where the water flows over the top) installed directly in the channel and cause water to back up behind the weir. Water must flow over the weir and flow freely like a waterfall. When that happens, there is what is called "critical depth" over the weir. When there is critical depth, there is a direct mathematical relationship between the water depth and the flow rate.

There are many types of weirs. Common ones are listed above. A v-notch weir is usually used for low flow rates and, due to its "V" shape, has more accuracy than other weir types at low flows. The flow rate over a v-notch weir increases with water depth to the 2.5 power.

For larger flows, rectangular weirs are most common. Flow rate over a rectangular weir increases with water depth to the 1.5 power. Cipoletti weirs are like rectangular weirs but the walls flare slightly outward. They are not nearly as common as v-notch or rectangular weirs.

Thank you for your interest in the LMNO Engineering newsletter,

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.

Pump Inlet Conditions

I recently presented a live webinar for the Society of Piping Engineers and Designers (SPED - https://www.spedweb.com, video at https://youtu.be/wXXpFtrg_GQ). I discussed fluid flow calculations for pressurized pipes. A topic that came up was pump inlet conditions, cavitation, and net positive suction head.

Most pumps for liquids require a certain amount of head at the inlet so that the pump inlet pressure is greater than the vapor pressure of the liquid. If the pressure drops below the liquid's vapor pressure, then the liquid will vaporize. As the liquid/vapor mixture flows through the pump, alternating pressure increases and decreases occur. This can cause a rapid alternating succession of liquid flashing to vapor and vapor re-condensing to liquid. This sequence is called cavitation and can completely ruin a pump due to rapid wear and tear of internal pump surfaces.

If cavitation can cause a problem for a given pump, the pump specifications will indicate the net positive suction head required (NPSHr) for the pump. This value is provided in length units, such as meters or feet, often spoken as "meters of head" or "feet of head." To determine the net positive suction head available (NPSHa) at the pump inlet, an engineering analysis of the piping system upstream of the pump inlet is required.

The piping system upstream of the pump includes the liquid source (possibly a tank open to the atmosphere or pressurized), fittings from the tank to a pipe, pipe lengths, pipe diameters, pipe materials, elbows, possibly valves (though be careful with these on inlet side of a pump), pipe reducers, elevation of the liquid source, elevation of the pump inlet, tank pressure, atmospheric pressure, liquid density, liquid vapor pressure, and liquid flow rate.

This information is input to the energy equation. The pump inlet head (absolute pressure head plus velocity head) is computed. Then the vapor pressure of the liquid (expressed in head units) is subtracted from this value and the result is NPSHa. Please see https://www.LMNOeng.com/Pipes/DWpump.php for the equation.

Please let me know if you have questions about net positive suction head. Thank you for your interest in the LMNO Engineering newsletter,

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.

Gradually Varied Flow - more discussion
https://www.LMNOeng.com/Channels/gvf.php

If you work or study in the discipline of open channel flow hydraulics, then you might have a need for a gradually varied flow (GVF) calculator. Our GVF calculator determines water depths with distance upstream or downstream in a trapezoidal open channel under steady flow conditions.

The calculator models channels that have a constant discharge, bottom width, side slopes, and Manning roughness coefficient. Depending on whether flow is subcritical or supercritical, the known depth (boundary condition) is entered either at the downstream or upstream end of the channel.

The calculator is based on mass and energy conservation equations. Starting at the boundary condition, the calculations proceed upstream or downstream using a finite difference approach. The Manning equation is used to compute energy slope (water surface elevation slope) at each distance position.

Sometimes there is confusion between GVF and uniform flow. In uniform flow, the water depth is constant along the length of the channel. This is a decent approximation for long channels having a constant cross-section and Manning n. If flow is uniform, the GVF calculator is not necessary. In the GVF calculator, one can enter the boundary condition as the uniform flow depth (also known as the "normal depth"). However, this is not very interesting since all of the computed depths along the channel will be the same. The GVF calculator's value lies in allowing one to enter a boundary condition that is not the uniform flow depth, and then computing the water surface profile.

Our gradually varied flow calculator at https://www.LMNOeng.com/Channels/gvf.php has a demonstration mode with graphical and tabular output.

Please let me know if you have questions. Thank you for your interest in the LMNO Engineering newsletter,

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

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