Hydraulics of Storm Sewers

Bernoulli Equation

Figure 16: Terms in Bernoulli Equation

The Bernoulli equation is the basic equation used to balance the energies associated with gradually varied flow through prismatic channels. While the velocity (V) and datum (Z) data is generally known, most of the effort in the design of storm sewer revolves around estimating the losses (hl1-2).

Friction Losses

The equations relating to friction loss have been discussed in Chapter 2. The friction slope is typically back computed based on the velocity or discharge and the known cross sectional properties of the channel.

Transition Losses

Transition losses occur when storm water enters the sewer system and encounters hydraulic structures such as manholes, bends, contractions, and enlargements. Each hydraulic structure that is encountered will result in a loss defined as:

Where K is a loss coefficient.

Contraction Losses

V2 > V1

Expansion Losses

V1 > V2

Where V1 is upstream velocity and V2 is downstream velocity.

Manhole Losses

In straight through situations where there are no changes in pipe size and the slope remains constant through the manhole:

Entrance Losses

The coefficient for entrance losses depends of the conduit. See Appendix for a list of coefficients used by the program.

Junction Losses

Losses at junctions were there are one or more incoming laterals:

Where D1 and D2 are the approach pipe diameters and is the angle between them.

Bend Losses

Bend Losses are estimated from

Where,

=central angle of bend in degrees

For angles less than 40 degrees. If the angle is greater than 40 degrees, it can be estimated from the following Chart.

Figure 17: Sewer Bend Loss Coefficient

Direct Step Profiles

StormShed3G™ uses a direct step profile computation when flow profiles are needed. Generally, this will be for culverts and other reaches. The direct step method is fairly straightforward and can be duplicated on spreadsheets with a little work. While a full discussion of the theory behind the procedure is outside of the scope of this manual, an example of the spreadsheet process is in order. Given the geometry of a reach, the flow rate (cfs) roughness and slope, the steps for filling out a spreadsheet is as follows:

Y	A	R		V		E		Sf				X
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)

Column	Description
Col 1.	Depth of flow in ft.
Col 2.	Water area in s.f. corresponding to the depth y in column 1.
Col 3.	Hydraulic radius in ft corresponding to y in column 1.
Col 4.	Four-thirds power of the hydraulic radius.
Col 5.	Mean velocity in fps obtained by dividing the flow rate by the water area in column 2.
Col 6.	Velocity head in ft.
Col 7.	Specific energy in ft obtained by adding the velocity head in column 6 to the depth of flow in column 1.
Col 8.	Change of specific energy in ft, equal to the difference between the E value in column 7 and that of the previous step.
Col 9.	Friction slope computed by solving for the slope using Manning’s equation, using values from columns 4 and 5.
Col 10.	Average friction slope between the steps, equal to the arithmetic mean of the friction slope just computed in column 9 and that of the previous step.
Col 11.	Difference between the bottom slope and the average friction slope.
Col 12.	Length of the reach in ft between the consecutive steps computed by dividing the value in column 8 by the value in column 11.
Col 3.	Distance from the section under consideration to the starting point of the computation.

The procedure is taken from Chow, Open Channel Hydraulics, McGraw-Hill Book Company, New York, 1959.