Takeaway: When designing sewers, engineers must first determine the hydraulic radius by calculating the cross-sectional area against the wetted perimeter. Designing a new sewer system is no easy feat. Engineers must consider several factors including the area, slope of the sewer and pipe diameter. However, one area that is crucial to their calculations is the hydraulic radius of their sewer design. Without this valuable piece of information, designers cannot complete their work.

The hydraulic radius of a pipe is the channel property which controls water discharge. The radius used helps to determine how much water and sediment can flow through the channel.

The higher the radius of a pipe, the larger the volume of fluid the line carries. There are no directly measurable characteristics of the hydraulic radius. However, it is directly related to the geometric properties of the channel in use. There are different ways to calculate the hydraulic radius. Unlike with other circular objects, the hydraulic radius of the pipe is not half the diameter of the channel. Instead, for a circular tube, a line being fully round with no openings on top or bottom, the hydraulic radius is equal to a quarter of the diameter.

To determine the hydraulic radius of a pipe, one must calculate the ratio of the cross-section to the wetted perimeter. The wetted perimeter is the portion of the cross-section which is wet. The equation reads as such:. There is a second way to calculate the hydraulic radius of a full circular pipe. Instead of using the cross-sectional area, one uses the pipe diameter to help in the calculation.

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This equation is as follows:. Hydraulic radius is not constant. The cross-sectional area of the pipe may remain the same throughout. However, the wetted perimeter may decrease. As the sewer line fills with liquid, less of it becomes in contact with the edges. With the wetted perimeter reduced, the hydraulic radius increases. The equation above shows the increase in radius. This increase occurs farther and farther downstream from the entry point of the sewer. As such, the velocity of the flow increases as the sewage moves farther downstream.

There are many calculations required to design a sewer. The design should be so that the pipes can carry sewage by relying on gravity to do the work.

These gravity sewers have a continuous gradient moving downward from the collection point to the outfall point. At the outfall point, however, the sewage lines move upward to allow the contents to enter a treatment plant for proper disposal. To learn about sewer maintenance, see Trenchless Sewer Repair and Cleaning Engineers designing a new sewage system, or planning rehabilitation of an existing site, must use the hydraulic radius to help calculate the flow velocity of the stormwater.

The sewage must maintain a minimum velocity to have a self-cleaning effect. Without the self-cleansing each day, deposits may build up and cause an obstruction. As the hydraulic radius changes downstream, the velocity also changes. Several calculations are required to ensure proper construction is in place.The hydraulic radius is defined as the area of flow in a pipe or conduit divided by the wetted perimeter.

The hydraulic radius is used as a measure of the efficiency of the conduit for transporting a fluid. As fluid flows through a conduit it loses energy due to the friction between the fluid and the sides of the conduit. Therefore the smaller the length of conduit in contact with the fluid, the less energy is lost due to friction and therefore the more efficiently the fluid is able to flow.

The effects of the hydraulic radius can be seen in the below diagram showing the velocity and flow achieved through a pipe with a circular cross section. The graph starts to level off and even falls as the pipe becomes full. This is because as the pipe narrows at the top the wetted perimeter increases so much relative to the flow area the velocity and even the flow rate begins to decrease. This means that a circular cross section pipe can never flow full until it is already overloaded.

The hydraulic radius is used in drainage design to calculate and compare the flow in different shaped conduits. The Manning Formula includes the hydraulic radius directly as an input and for this reason Manning's equation is often used for calculating the flow in open channels and non-circular conduits.

Indeed so long as the flow is open ie not under pressure and the channel or conduit does not include any re-entrant corners or significantly asymmetrical features, the Manning equation can be used to estimate the flow through the conduit. A more accurate calculation known as the Colebrook-White Equation is also often used.

The Colebrook-White equation is theoretically more correct than the Manning equation but it does not include the hydraulic radius as an input. However, as the hydraulic radius for circular pipes running full is 4 times the pipe diameter, it is possible to substitute the pipe diameter input in the Colebrook-White equation for 4 times the hydraulic radius. In this way the Colebrook-White equation can be modified to accommodate non-circular conduits.

Non-circular conduits are often used to take advantage of their different hydraulic radii compared with circular pipes. Arch include a large flat bottom which allows greater flow through the pipe compared to a similar height circular pipe. Egg shaped or ovoid pipes include narrow bottoms allowing greater velocities of flow through the pipe at small flows levels improving the self-cleansing nature of the pipes compared to circular pipes.

These are explained in more detail here. The CivilWeb Pipe Flow Calculator spreadsheet calculates the hydraulic radius as part of the flow rate calculations. The spreadsheet suite includes design and analysis spreadsheets for circular, arch, ovoid and elliptical shaped pipes.

The suite also includes an geometric analysis tool for circular pipes which can calculate the hydraulic radius of the pipe at any height. The User Guide which is provided with the full license version of the spreadsheet also includes guidance on calculating the hydraulic radius for non-circular cross sections. This spreadsheet calculates the design runoff flow for a site in accordance with the a number of different methods including the Wallingford Procedure. Related Spreadsheets from CivilWeb. Pipe Flow Calculator. Manning Open Channel Design.The Manning formula is an empirical formula estimating the average velocity of a liquid flowing in a conduit that does not completely enclose the liquid, i.

However, this equation is also used for calculation of flow variables in case of flow in partially full conduitsas they also possess a free surface like that of open channel flow. All flow in so-called open channels is driven by gravity. It was first presented by the French engineer Philippe Gauckler in and later re-developed by the Irish engineer Robert Manning in In the United States, in practice, it is very frequently called simply Manning's equation.

Solving for Q then allows an estimate of the volumetric flow rate discharge without knowing the limiting or actual flow velocity.

The Gauckler—Manning formula is used to estimate the average velocity of water flowing in an open channel in locations where it is not practical to construct a weir or flume to measure flow with greater accuracy. The friction coefficients across weirs and orifices are less subjective than n along a natural earthen, stone or vegetated channel reach. Cross sectional area, as well as nwill likely vary along a natural channel. Accordingly, more error is expected in estimating the average velocity by assuming a Manning's nthan by direct sampling i.

Manning's equation is also commonly used as part of a numerical step methodsuch as the standard step methodfor delineating the free surface profile of water flowing in an open channel. The formula can be obtained by use of dimensional analysis.

In the s this formula was derived theoretically using the phenomenological theory of turbulence. Then, as the observation indicates that there is rotation in the fluids, the acceleration and torque must have disappeared by the time they were observed, and the angular velocity became constant.

Then, for an incompressible and Newtonian fluid, due to Helmholtz theoremwe can determine v. The hydraulic radius is one of the properties of a channel that controls water discharge. It also determines how much work the channel can do, for example, in moving sediment.

All else equal, a river with a larger hydraulic radius will have a higher flow velocity, and also a larger cross sectional area through which that faster water can travel. This means the greater the hydraulic radius, the larger volume of water the channel can carry. Based on the 'constant shear stress at the boundary' assumption,  hydraulic radius is defined as the ratio of the channel's cross-sectional area of the flow to its wetted perimeter the portion of the cross-section's perimeter that is "wet" :.

For channels of a given width, the hydraulic radius is greater for deeper channels. In wide rectangular channels, the hydraulic radius is approximated by the flow depth. The hydraulic radius is not half the hydraulic diameter as the name may suggest, but one quarter in the case of a full pipe. It is a function of the shape of the pipe, channel, or river in which the water is flowing.

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Hydraulic radius is also important in determining a channel's efficiency its ability to move water and sedimentand is one of the properties used by water engineers to assess the channel's capacity. The Gauckler—Manning coefficient, often denoted as nis an empirically derived coefficient, which is dependent on many factors, including surface roughness and sinuosity. When field inspection is not possible, the best method to determine n is to use photographs of river channels where n has been determined using Gauckler—Manning's formula.

In natural streams, n values vary greatly along its reach, and will even vary in a given reach of channel with different stages of flow. Most research shows that n will decrease with stage, at least up to bank-full.

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Overbank n values for a given reach will vary greatly depending on the time of year and the velocity of flow. Summer vegetation will typically have a significantly higher n value due to leaves and seasonal vegetation.

Research has shown, however, that n values are lower for individual shrubs with leaves than for the shrubs without leaves. High velocity flows will cause some vegetation such as grasses and forbs to lay flat, where a lower velocity of flow through the same vegetation will not.

In open channels, the Darcy—Weisbach equation is valid using the hydraulic diameter as equivalent pipe diameter. It is the only best and sound method to estimate the energy loss in human made open channels. For various reasons mainly historical reasonsempirical resistance coefficients e.Includes Excel Manning equation open channel flow calculator spreadsheets to make a variety of open channel flow calculations with the Manning Equation in U.

Scroll down for more details about these spreadsheets in U. The spreadsheets in this bundle all use U. The spreadsheets in this bundle all use S. Calculations are in U. Calculations are in S. This group of Excel spreadsheets includes all of the spreadsheets in the Manning Equation and Open Channel Flow Meas Bundle described above ; and those in the NonUnif and Critical Open Chan Flow Bundle spreadsheets for hydraulic jump calculations, critical depth and critical slope calculations, M-1 surface profiles, and calculations of non-uniform flow surface profiles.

This group of Excel spreadsheets includes all of the spreadsheets in the Manning Equation and Open Channel Flow Measurement Bundle described above ; and those in the NonUnif and Critical Open Chan Flow Bundle spreadsheets for hydraulic jump calculations, critical depth and critical slope calculations, M-1 surface profiles, and calculations of non-uniform flow surface profiles.

This set of Excel spreadsheets makes it easy to calculate the hydraulic radius for open channel flow in a triangular, rectangular, or trapezoidal channel, or in a circular pipe flowing partially full either less than half or more than half full. These calculations are in U. This Excel spreadsheet calculates the volumetric flow rate and average velocity for open channel flow in a triangular channel for specified channel side slope, flow depth, Manning roughness coefficient, and channel bottom slope.

The calculations are in either U. These spreadsheets use U. These normal depth open channel flow Excel Spreadsheets include those for calculating normal depth in rectangular, trapezoidal, or triangular channels. The calculations use U. These hydraulic radius calculator Excel spreadsheets makes it easy to calculate the hydraulic radius for open channel flow in a triangular, rectangular, or trapezoidal channel, or in a circular pipe flowing partially full either less than half or more than half full.

These calculations are in S. These spreadsheets use S. This set of Excel Spreadsheets includes those for calculating normal depth in rectangular, trapezoidal, or triangular channels. The calculations use S.

This Excel spreadsheet template can be used to determine the Manning roughness coefficient for a natural channel based on a description of various aspects of the channel, such as its irregularity, cross section variations, the effect of obstructions, the effect of vegetation, and degree of meander.

This spreadsheet is based on a method developed by W.The CivilWeb Pipe Flow Calculator spreadsheet is an advanced drainage design and analysis spreadsheet which can calculate the flow rate through a drainage pipe using either the Colebrook-White equation or the Manning Equation. The spreadsheet includes unique design features to make detailed drainage pipe design quicker and easier than ever. The spreadsheet suite includes two main sheets, one used for designing new drainage pipes and one used for analysis of an existing drainage pipe.

The design spreadsheet allows the user to simply specify the required flowthe maximum and minimum velocity and the pipe roughness. The spreadsheet then calculates the standard pipe sizes and gradients which match the required flow rate at an acceptable velocity.

The designer can see at a glance all the suitable pipe sizes and gradients which meet the design conditions. The designer can then input a pipe of any size and gradient for analysis. The spreadsheet calculates the pipes maximum flow and velocity as well as the flow and velocity of the pipe running full.

### Manning formula

These are then checked against the design conditions. Note that design conditions are usually only compared against the values for the pipe running full. This is generally a convention designed to simplify the calculations but with advanced software such as this spreadsheet the design conditions can easily be checked against the maximum value as well as the pipe full values. The spreadsheet also presents a design graph for this pipe and gradient showing the flow rate and average velocity at any height of flow.

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This information is essential if the pipe is not designed to run full, velocity and flow rates can easily be determined from the graph at any water height. This unique design sheet enables the user to complete drainage pipe design in seconds, quicker than any other software on the market. The pipe analysis sheet allows the designer to create bespoke design graphs based on the specific pipe roughness values required.

This graph can be used to quickly evaluate the suitability of different pipe sizes and gradients. This sheet also creates a graph showing the flow rate and velocity at different water heights and allows the user to calculate precise values for these parameters at any specified water height level in the pipe.

Each of these design spreadsheets includes a Colebrook-White and Manning Equation version. Along with the main design spreadsheets for pipe design and analysis, the CivilWeb Pipe Flow Calculator suite includes a number of other useful design tools. Additional Calculation Tools Included Along with the main design spreadsheets for pipe design and analysis, the CivilWeb Pipe Flow Calculator suite includes a number of other useful design tools; Non-Circular Cross Section Analysis - A tool is included completing the same analysis but for common non-circular pipe cross sections such as arch, ovoid or elliptical pipes.

There is also a calculator tool for analysis of non-standard pipe dimensions using the hydraulic radius and the wetted perimeter for analysis of the pipe cross section.We believe that all fire protection engineers should have a good understanding of the principles of hydraulic calculations to enable them to optimize designs and to ensure that all calculations can be properly checked and verified.

Fire sprinkler engineers, inspectors, and insurance companies will find a use for our free Hcalc - Hydraulic Calculator. It can be used for teaching the principals of hydraulics in fire protection engineering, checking calculations or for solving simple hydraulic calculations for fire sprinkler, hydrant, hose reel and other types of water-based fire protection systems. Fire protection engineers and consulting engineers from around the world have installed Hcalc to help them with calculations and the verifica.

With Hcalc you can calculate the friction loss in a circular pipe using the Hayes and Williams pressure loss formula which is specified in NFPA 13 and EN and in many other international design standards. You can specify the pipe size, flow rate, and the pipes C-factor and Hcalc will calculate the pressure loss per meter and for the total pipe length and the water velocity. You can select the type of pipe material from the drop-down list or enter your own pipe C-factor. Whenever you need to carry out pressure loss calculation or to verify the simple calculator is ready to help.

With Hcalc - Spk Flow you can solve any of the three variables in the K-Factor formula, the flow from the sprinkler, the pressure required at a sprinkler and the K-Factor without the need of remembering the formula. The K-factor formula is one of the basic building blocks of fire sprinkler design and fire protection hydraulic calculations, most of us will have committed it to memory but now with Hcalc you know longer need to.

You can have this simple tool sitting on your desktop so you no longer need to find your calculator or pen and paper. You can use Hcalc any type of fire sprinkler or water mist nozzle or in fact any other nozzle or head which you have a K-Factor, this could be a hose reel nozzle, a foam monitor or a fire hydrant.

Hcalc is easy to use but will have still provided an on-line user manual and a short video tutorial to help get you started. You will also find all the formulas which have been used clearly set out and with additional information. If you're interested in learning more about hydraulic calculations for fire sprinkler systems would like to know how to carry out calculations for a simple tree end fed systems using the time honoured longhand method with paper and pen, then you may find our article how to calculate a fire sprinkler system to be of interest.

We personally would not recommend this method anything more than a very simple system as by its nature will very likely to make an error somewhere in the calculation which is then compounded as you move along. Our FHC hydraulic calculation software is ideal for carrying out some calculations from the simplest to the most complicated system design.

Hcalc for fire sprinkler hydraulic calculations. Download Hcalc give it a try today for free! Download Hcalc. Pipe pressure loss calculations. Hazen Williams pressure loss formula With Hcalc you can calculate the friction loss in a circular pipe using the Hayes and Williams pressure loss formula which is specified in NFPA 13 and EN and in many other international design standards.

Flow from a fire sprinkler head. Sprinkler head - K-factor calculation With Hcalc - Spk Flow you can solve any of the three variables in the K-Factor formula, the flow from the sprinkler, the pressure required at a sprinkler and the K-Factor without the need of remembering the formula.

Hydraulics for engineers. Find out more. Instruction Manual. Hydraulic calculation for fire sprinkler systems If you're interested in learning more about hydraulic calculations for fire sprinkler systems would like to know how to carry out calculations for a simple tree end fed systems using the time honoured longhand method with paper and pen, then you may find our article how to calculate a fire sprinkler system to be of interest.

Facebook Twitter Linkedin.Scroll down on each category page to see all of the articles. Similar blog articles are available at our companion site, www. This Excel spreadsheet is intended for calculating the flow rate. You can buy a convenient spreadsheet for viscous liquid partially full pipe flow for a very reasonable price. It is available in either U. Read on for background information about a spreadsheet for viscous liquid partially full pipe flow.

That post describes the use of the Manning Equation, which can only be used for the flow of water. The parameters and equations for calculating them for partially full pipe flow are shown in the diagram below for flow at a depth greater than the pipe diameter. The definition of hydraulic radius and the Darcy-Weisbach equation as applied to partially full pipe flow are shown below.

This Excel spreadsheet can be used to calculate the pipe flow rate, required diameter, depth of flow or pipe slope for partially full pipe flow of a viscous liquid. This Excel spreadsheet, as well as others for pipe flow and open channel flow calculations, is available in either U. Bengtson, Harlan H. Steel, E. Bengtson, H. Scroll down for the following blog articles in this category:. Read on for information about Excel spreadsheets that can be used as Manning equation open channel flow calculators.

An excel spreadsheet can conveniently be used as a Manning equation open channel flow calculator. The Manning equation can be used for water flow rate calculations in either natural or man made open channels.

Image Credit: geograph.

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Open channel flow may be either uniform flow or nonuniform flow, as illustrated in the diagram at the left. The diagram above shows a stretch of uniform open channel flow, followed by a change in bottom slope that causes non-uniform flow, followed by another reach of uniform open channel flow.

The Manning Equation, which will be discussed in the next sectioncan be used only for uniform open channel flow. The Manning Equation is:. It should be noted that the Manning Equation is an empirical equation. The U. All calculations with the Manning equation except for experimental determination of n require a value for the Manning roughness coefficient, n, for the channel surface.

This coefficient, n, is an experimentally determined constant that depends upon the nature of the channel and its surface.

Smoother surfaces have generally lower Manning roughness coefficient values and rougher surfaces have higher values. Many handbooks, textbooks and online sources have tables that give values of n for different natural and man made channel types and surfaces. The table at the right gives values of the Manning roughness coefficient for several common open channel flow surfaces for use in a Manning equation open channel flow exce l spreadsheet. 