Following the initial “just-full” storm drain design, the system is analyzed using energy-momentum theory to account for specific energy losses. This method allows for the calculation of hydraulic and energy grade lines (HGL and EGL) for a given storm drain line by starting with the water surface elevation of the outfall and working upstream, accounting for all losses due to pipe friction, manholes, transitions, bends, junctions, and pipe entrances and exits. In cases where pressure flows exist, certain limitations exist on the maximum elevation of the EGL in relation to the ground surface (finished grade). Compliance with minimum and maximum flow velocities is based on peak design flow in the final selected pipe size for each segment. See GJMC §
28.40.020 through
28.40.060 for specific design criteria.
Energy-momentum theory is based upon the concept that energy, typically expressed in hydraulics as “head” in a linear dimension such as feet, is conserved along a given conduit segment. For a segment where A is the upstream end and B is downstream, the steady-flow energy equation can be expressed as:
Where:
z | = | Invert Elevation above any Horizontal Datum (ft.) |
p | = | Fluid Pressure lbf/ft.2 |
γ | = | Specific Weight of Water ≅ 62.4 lbf/ft.3 |
V | = | Flow Velocity (fps) |
hP | = | Head Added by a Pump (if applicable) (ft.) |
ΣhL | = | Sum of Head Losses in Segment A – B as calculated per the methods prescribed in this section |
Each term in Equation 28.40-4, and thus the sum of the formula, has a linear dimension (e.g., feet). Each term represents the hydraulic head contributed to the total energy head by that term. For instance, the third term, V2/2g, is the velocity head. The EGL elevation at a given point is equal to:
and the HGL elevation is simply the EGL minus the velocity head:
In cases where outfall water surface is equal to or higher than the outlet flow elevation, the EGL and HGL are assumed to be equal, i.e., velocity is zero at the downstream point where calculations start. However, if the outfall water surface is lower than the outlet pipe flow elevation, the latter value is used as the outlet HGL. Note that the outfall water surface elevation used must be determined coincident with the time of peak flow from the storm drain.
The HGL at the next structure (e.g., manhole) is determined by the equations presented in Table 28.40.090(a). The equations are separated by HGL at the pipe inlet downstream of the manhole and the pipe outlet at the inlet to the manhole. For nonsurcharged flow (less than 80 percent pipe depth), the free water surface at the pipe inlet (downstream end of the manhole) is added to head loss across the manhole to find the pipe outlet HGL (upstream end of the manhole).
Table 28.40.090(a): Equations for Determining HGL |
|---|
Surcharge Conditions | Outlet Submergence | HGL in Manhole/Junction | At | Equation Number |
|---|
dn/D > 0.80 | N/A | = HGLPipe Outlet + hf + hminor | Pipe Inlet (D/S from MH) | 28.40-7 |
dn/D > 0.80 | N/A | = HGLPipe Inlet + hmh | Pipe Outlet (U/S from MH) | 28.40-8 |
dn/D ≤ 0.80 | Unsubmerged | = WSEPipe Inlet | Pipe Inlet (D/S from MH) | 28.40-9 |
dn/D ≤ 0.80 | Unsubmerged | = WSEPipe Inlet + hmh | Pipe Outlet (U/S from MH) | 28.40-10 |
dn/D ≤ 0.80 | Submerged | = Larger of Equations 28.40-7 and 28.40-9 OR = Larger of Equations 28.40-8 and 28.40-10 |
Where:
dn | = | Normal Flow Depth in Pipe (feet) |
HGLPipe Outlet | = | Larger of Tailwater Elevation, Flow Depth Elevation at Pipe Outlet, and HGL at Next Downstream Pipe Inlet |
WSEPipe Inlet | = | Free Water Surface Elevation at Pipe Inlet |
hf, hmh, h minor | = | Head Losses as Described in This Section |
Occasionally, design flow through a pipe may be not only gravity-flow (nonsurcharged) but also supercritical. Pipe losses (hf and hminor) in a supercritical pipe section are not carried upstream. (HEC-22)
In locations where two adjoining pipe segments flow in supercritical conditions, manhole losses are also ignored for that line. The designer shall be careful to include these losses where only one of the pipes on the line under investigation contains supercritical flow.
Inlet pipes to a manhole must occasionally have an invert significantly above that of the outlet pipe. In locations where the outlet pipe water surface elevation (or HGL if pressure flow) is below the invert of an inlet pipe, that inlet pipe is treated as an outfall pipe. In this case, the outfall water surface elevation is always lower than the pipe outlet water level, so the latter elevation is used for the initial HGL of the new upstream reach. The outflow pipe from the manhole in such a situation acts as a culvert under either inlet or outlet control. See Chapter
28.48 GJMC and/or FHWA
Hydraulic Design of Highway Culverts (HDS-5) for information regarding the computation of an HGL at the manhole and calculation of head loss due to a culvert inlet.
The following subsections prescribe methods for determining the energy losses induced by pipe friction, manholes, and other structures (minor pipe losses) that may be encountered by storm drain flows.
(a) Pipe Friction Losses.
Pipe friction is a significant source of energy dissipation in storm drains, whether in gravity-flow or pressure-flow conditions. For the former, friction slope (Sf) can be assumed to be equal to the slope of the pipe invert (So). For pipes with a surcharge flow condition (dn/D > 0/80), Equations 28.40-11 and 28.40-12 define friction slope (units for variables are the same as in Equation 28.40-1 when using English units).
Where:
KQ | = | 2.21 (English Units) |
KQ | = | 1.0 (S.I. Units) |
Where:
KQ | = | 0.46 (English Units) |
KQ | = | 0.312 (S.I. Units) |
Equation 28.40-11 is a form of the Chezy-Manning formula, and is based on average velocity in the pipe segment. Since flow rate and cross-sectional area typically remain constant through one segment of pipe, average velocity can be assumed to equal flow rate divided by flow area. Where flow rate and/or pipe size changes within one segment (such as at a pipe transition without a manhole or a no-access junction), this velocity is the average of those calculated at the ends of the pipe segment (Linsley, 1992). Equation 28.40-12 is based on the average flow rate in the pipe segment.
Once the friction slope is known, pipe friction head loss is calculated by multiplying the friction slope by the pipe segment length:
(b) Manhole Junction Losses.
This subsection details the energy-loss method used by the HYDRAIN program (FHWA) as presented in HDS-4 for calculation of approximate head loss through a manhole. This method applies to any junction of two or more pipes accessible by a manhole. The approximate head loss coefficient values presented in Table 28.40.080 are replaced by the values computed herein.
For each manhole, the designer must first calculate the initial head loss coefficient (Ko) and all applicable coefficient correction factors (Cx). The adjusted head loss coefficient (K) and head loss in the manhole (hmh) are then computed.
| (28.40-14) |
| (28.40-15) |
| (28.40-16) |
Where:
θ | = | Angle Between Inflow and Outflow Pipes (≤ 180°) |
b | = | Manhole of Junction Diameter (at water level) |
Do | = | Outlet Pipe Diameter |
The coefficient correction factors are calculated using the equations presented below and are applied to the initial head loss coefficient per Equation 28.40-15. Note that some correction factors do not apply to all manhole configurations. These nonapplicable factors are set to unity.
(1) CD – Correction Factor for Pipe Diameter. This applies to pressure flow when the ratio of water depth in the manhole above the outlet pipe invert to outlet pipe diameter is greater than 3.2. dmho/Do > 3.2.
Where:
Do | = | Outlet Pipe Diameter |
Di | = | Inlet Pipe Diameter |
(2) Cd – Correction Factor for Flow Depth. This applies to gravity flow and low-pressure flow when the ratio of water depth in the manhole above the outlet pipe invert to outlet pipe diameter is less than 3.2. dmho/Do < 3.2.
Where:
Dmho | = | Water Depth in Manhole Above Outlet Pipe Invert |
Do | = | Outlet Pipe Diameter |
For purposes of this calculation, water depth in the manhole is approximated as the vertical distance from the outlet pipe invert to the HGL at the upstream end of the outlet pipe. |
(3) CQ – Correction Factor for Relative Flow. This applies to manholes with three or more pipes entering the structure at similar elevations (one of these pipes will be the outlet pipe). This correction factor does not apply to the effects of inflow pipes with flowlines far enough above the outlet pipe to qualify as plunging flow (see Equation 28.40-20 and explanation, this section).
Where:
θ | = | Angle Between the Inflow Pipe of Interest and the Outflow Pipe |
Qi | = | Flow in the Inflow Pipe of Interest |
Qo | = | Flow in the Outflow Pipe |
The “pipe of interest” is the inlet pipe to the manhole on the line being investigated. This factor accounts for streamline interference by flow from other pipes entering the manhole. See Figure 28.40.090(a) for an illustration of the relative flow effect.
(4) Cp – Correction Factor for Plunging Flow. This applies to manholes with an inflow pipe of interest that is affected by plunging flow from another inflow pipe with a higher flowline. The factor does not apply to the line with the pipe that is discharging the plunging flow, and only applies when the height of the plunging-flow pipe flowline above the outlet pipe center exceeds the manhole water depth above the outlet pipe invert: h > dmho
Where:
h | = | Vertical Distance of Plunging Flow (height of plunging flow pipe flowline above center of outlet pipe) |
dmho | = | Water Depth in Manhole Above Outlet Pipe Invert |
Do | = | Outlet Pipe Diameter |
A common application of this correction factor occurs at locations where inlets convey intercepted flow directly (vertically) to the storm drain main line (drop inlets) or where laterals enter a manhole well above the main line invert.
(5) CB – Correction Factor for Benching. This applies to all flow conditions. See Figure 28.40.090(b) and Table 28.40.090(b) for proper correction factor selection.
Table 28.40.090(b): Benching Correction Factors |
|---|
Bench Type (see Figure 28.40.090(b)) | Outlet Pipe Conditions |
|---|
Fully Submerged, Pressure Flow* | Unsubmerged, Free Surface Flow** |
|---|
Flat or Depressed | 1 | 1 |
Benched: 1/2 Pipe Diameter | 0.95 | 0.15 |
Benched: 1 Pipe Diameter | 0.75 | 0.07 |
Improved Bench | 0.4 | 0.02 |
Adapted from Mesa County SWMM 1996, Figure “H-4” *Applies for dmho/Do ≥ 3.2 **Applies for dmho/Do ≤ 1.0 |
As can be seen in Table 28.40.090(b), benching in manholes significantly reduces head loss due to outlet inefficiency, especially in unsubmerged conditions. Note that in this case, the submerged pressure-flow factors do not apply until flow depth in the manhole has exceeded 3.2 times the outlet pipe diameter. Therefore, for depths between free surface (gravity) flow and full pressure-flow conditions (1.0 > dmho/Do < 3.2), the designer shall use a linear interpolation to compute the benching correction factor.
(c) Minor Pipe Losses.
This subsection describes the methods used in Mesa County for the calculation of head losses caused by pipe transitions (expansions or contractions), bends (curved drains), no-access junctions, on-grade inlets, and exits (outlets). The minor losses are added together for a given pipe segment per Equation 28.40-21:
(1) he and hc – Transition Losses. Transition losses occur when pipe size is changed at a location other than a manhole. Expansions may be necessary due to changes in flow rate or slope. Contractions are locations where pipe size is decreased, and are allowed only through a variance. Methods for head loss calculation through a pipe contraction are included in this title.
The calculation of head loss through a transition differs for nonpressure flow and pressure flow.
(i) Nonpressure Flow Transitions.
Where:
Ke | = | Expansion Coefficient (see Table 28.40.090(a)(1)) |
Kc | = | Contraction Coefficient (see Table 28.40.090(a)(2)) |
Kc | = | 0.5 · Ke for Gradual Contractions |
V1 | = | Velocity Upstream of the Transition |
V2 | = | Velocity Downstream of the Transition |
(ii) Pressure-Flow Transitions.
Where:
Kep | = | Expansion Coefficient (see Table 28.40.090(b)(1), (2)) |
Kcp | = | Contraction Coefficient (see Table 28.40.090(b)(3)) |
V1 | = | Velocity Upstream of the Transition |
V2 | = | Velocity Downstream of the Transition |
See Figure 28.40.090(c) for illustration of the “Angle of Cone” variable used in Tables 28.40.090(a) and 28.40.090(b). |
TABLE 28.40.090(b) (PAGE 1 of 2) |
TABLE 28.40.090(b) (PAGE 2 of 2) |
(2) hb – Bend Losses (Curved Drains). The minor loss that accompanies a storm drain bend can be approximated by:
Where:
Δ | = | Angle of Curvature (degrees) |
This equation does not apply to bends located at manholes. Head losses due to manhole bends and deflections are addressed in subsection
(b) of this section.
(3) hj – No-Access Junctions. This term applies to head loss associated with locations where a lateral pipe connects to a larger trunk pipe without the use of a manhole structure. While these junctions are not recommended for trunk pipes of less than 48 inches in diameter, it is sometimes physically or economically inefficient to place a manhole at every junction location. At locations where more than one lateral joins the main line (trunk), a manhole is required. The head loss at no-access junctions is related to the relative flows and velocities of all three pipes, the angle between the lateral and trunk pipes, and the cross-sectional area of the trunk pipe.
Where:
Qo, Qi, QL | = | Outlet, Inlet and Lateral Flow Rates |
Vo, Vi, VL | = | Outlet, Inlet and Lateral Velocities |
hvo, hvi | = | Outlet and Inlet Velocity Heads = V2/2g |
Ao, Ai | = | Outlet and Inlet Cross-Sectional Areas |
θ | = | Angle of Lateral with Respect to Outflow Pipe |
(4) h
i – On-Grade Inlets (Culvert-Type Inlets). In some locations, water may enter a storm drain system from a drainage channel, overflowing pond, or other conveyance with a flowline approximately equal to that of the storm drain inlet. These storm drain entrances are hydraulically equivalent to culvert inlets, thus the coefficient K
i in Equation 28.40-28 is equal to the culvert entrance loss coefficient K
e provided in Chapter
28.48 GJMC, Table 28.48.110. (Note that K
e represents the expansion loss coefficient in this chapter.)
Where:
Ki | = | On-Grade Inlet Coefficient (see Table 28.48.110) |
(5) ho – Outlets (Pipe Exits). This term applies to pipe outlets other than those which exit to a manhole. Outlet losses are always associated with a storm drain system outfall to an open channel, detention/retention basin, or other receiving waters. Outlets that discharge into a body of water with essentially zero velocity in the direction of the storm drain exit lose all velocity (one velocity head). This includes outlets perpendicular to an open channel and all submerged outlets. The storm drain flow is also assumed to lose all velocity when it discharges to open air and plunges to the receiving waters.
Where:
Vo | = | Flow Velocity at Storm Drain Exit |
Vd | = | Flow Velocity (in the direction of storm drain flow) in Receiving Waters |
Allowable storm drain velocities often differ from those for open channels. Chapters
28.32,
28.36 and
28.48 GJMC present criteria for the proper design of outlets to open channels, including the design of riprap and other energy dissipation structures to reduce channel scour potential.
(Res. 40-08 (§ 1003.2), 3-19-08)
