Hydraulic Radius Explained: Sewer Design, Formulas and Perimeter Calculations
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. (For more on sewers, check out The Complex World of Sewer Networks.)
What Is a Hydraulic Radius?
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.
How Is the Hydraulic Radius Calculated?
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:
Rh = A/P
Rh is the hydraulic radius.
A is the cross-sectional area.
P is the wetted perimeter.
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. This equation is as follows:
R is the hydraulic radius.
D is the diameter of the pipe measured in either meters or feet.
How Does the Hydraulic Radius Change?
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. For example, using the equation Rh = A/P:
Rh = 28/15 = 1.87
However, when the wetted perimeter is decreased to 10:
Rh = 28/10 = 2.8
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.
What Role Does Hydraulic Radius Play in Sewer Design?
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 101.)
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. The sewer’s maximum speed should also be calculated to limit the interior damage on the sewage pipes.
As the hydraulic radius changes downstream, the velocity also changes. Several calculations are required to ensure proper construction is in place.
When determining the velocity, engineers employ the Manning formula. The formula reads as:
V is the cross-section’s average velocity.
K is the conversion factor between SI and English units.
The coefficient n represents the Gauckler-Manning coefficient. Both k and n may be left out of the equation if there is a notation of the correct units while calculating the radius.
Rh is the hydraulic radius with S being the slope of the hydraulic grade.
Before calculating the velocity to ensure that the correct slope and diameter of the pipes are adequate, engineers must correctly estimate the amount of sewage discharge the new sewer lines are expected to encounter. Using this value, the planners can select the appropriate size pipelines to handle estimated waste discharge. Planners should also plan to bury lines at least two to three meters deep to carry waste from subterranean structures such as basements effectively.
Sewer design requires many elements to ensure there is no overflow and limit the potential for health hazards in the area it services. Understanding how the hydraulic radius applies to the flow of waste discharge is the only way for engineers to correctly calculate the pipe size, slope and expected velocity of the stream.