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Section 7: Conduit Systems Energy Losses

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Minor Energy Loss Attributions

Major losses result from friction within the pipe. Minor losses include those attributed to junctions, exits, bends in pipes, manholes, expansion and contraction, and appurtenances such as valves and meters.

Minor losses in a storm drain system are usually insignificant. In a large system, however, their combined effect may be significant. Methods are available to estimate these minor losses if they appear to be cumulatively important. You may minimize the hydraulic loss potential of storm drain system features such as junctions, bends, manholes, and confluences to some extent by careful design. For example, you can replace severe bends by gradual curves in the pipe run where right-of-way is sufficient and increased costs are manageable. Well designed manholes and inlets, where there are no sharp or sudden transitions or impediments to the flow, cause virtually no significant losses.

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Junction Loss Equation

For adjoining pipes to be considered a pipe junction, the node and only two inflow pipes (a lateral and a trunk) may enter the junction. The minor loss equation for a pipe junction is in the form of the momentum equation. In Equation 10-38 the subscripts “i”, “o”, and “1” indicate the inlet, outlet, and lateral, respectively.

Equation 10-38.

where:

  • hj = junction head loss (ft. or m)
  • Q = flow (cfs or m3/s)
  • v = velocity (fps or m/s)
  • A = cross-sectional area (sq. ft. or m2)
  • = angle in degrees of lateral with respect to centerline of outlet pipe
  • g = gravitational acceleration = 32.2 ft/s2 or 9.81 m/s2.

The above equation applies only if vo > vi and assumes that Qo = Qi + Q1.

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Exit Loss Equation

The exit loss, ho, is a function of the change in velocity at the outlet of the pipe as shown in Equation 10-39.

Equation 10-39.

where:

  • v = average outlet velocity (fps or m/s)
  • vd = channel velocity downstream of the outlet (fps or m/s)
  • Co = exit loss coefficient (0.5 typical).

The above assumes that the channel velocity is lower than the outlet velocity

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Manhole Loss Equations

Calculate the loss from one pipe to another throught a manhole using Equation 10-40.

Equation 10-40.

where the adjusted head loss coefficient (K) is found with Equation 10-41.

Equation 10-41.

where:

  • KO = initial head loss coefficient based on relative manhole size
  • CD = correction factor for pipe diameter
  • Cd = correction factor for flow depth
  • CQ = correction factor for relative flow
  • CB = correction factor for benching
  • CP = correction factor for plunging flow.
  • The initial head loss coefficient (Ko) ) is estimated as a function of the relative manhole size and angle between the inflow and outflow pipes.

Equation 10-42.

where:

  • KO = initial head loss coefficient based on relative manhole size
  • = angle between the inflow and outflow pipes (see Figure 10‑20)
  • b = manhole diameter or width (ft. or m)
  • DO = outlet pipe diameter (ft. or m).

Angle Between Inflow and Outflow Pipes (click in image to see full-size image) Anchor: #i1006313grtop

Figure 10-20. Angle Between Inflow and Outflow Pipes

The correction factor for pipe diameter, CD, can be determined by the following:

Equation 10-43.

where:

  • CD = correction factor for variation in pipe diameter
  • DI = incoming pipe diameter (ft. or m)
  • DO = outgoing pipe diameter (ft. or m).

A change in head loss due to differences in pipe diameter is significant only in pressure flow situations when the depth in the manhole to outlet pipe diameter ratio, d/Do, is greater than 3.2. Therefore, only apply it in such cases; otherwise, use CD = 1.

Calculate the correction factor for flow depth, Cd, using Equation 10-44.

where:

  • Cd = correction factor for flow depth
  • d = water depth in manhole above outlet pipe invert (ft. or m)
  • DO = outlet pipe diameter (ft. or m).

This correction factor is significant only in cases of free surface flow or low pressures, when d/DO ratio is less than 3.2. Water depth in the manhole is approximated as the level of the hydraulic grade line at the upstream end of the outlet pipe.

Compute the correction factor for relative flow, CQ, using Equation 10-45.

Equation 10-44.

where:

  • CQ = correction factor for relative flow
  • = angle between the inflow and outflow pipes
  • Qi = flow in the incoming pipe (cfs or m3/s)
  • QO = flow in the outlet pipe (cfs or m3/s)
  • CQ = a function of the angle of the incoming flow as well as the percentage of flow coming in through the pipe of interest versus other incoming pipes.
  • To illustrate this effect, consider the following example (see Figure 10‑21):

  • Q1 = 0.3 m3/s
  • Q2 = 0.1 m3/s
  • Q3 = 0.4 m3/s

Example of Correction Factor for Relative
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Figure 10-21. Example of Correction Factor for Relative Flow

Solving for the relative flow correction factor in going from the outlet pipe (number 3) to one of the inflow pipes (number 2):

Equation 10-45.

For a second example, consider the following flow regime:

Q1=1 cfs

Q2=3 cfs

Q3=4 cfs

Calculating CQ for this case:

Equation 10-46.

In both of these cases, the flow coming in through pipe number 2 has to make a 90-degree bend before it can go out pipe number 3. In case 1, the larger flow traveling straight through the manhole from pipe number 1 to pipe number 3 assists the flow from pipe number 2 in making this bend. In case 2, a majority of the flow is coming in through pipe number 2. There is less assistance from the straight through flow in directing the flow from pipe number 2 into pipe number 3. As a result, the correction factor for relative flow in case 1 (0.19) is much smaller than the correction factor for case 2 (0.65).

The correction factor for plunging flow, Cp , is calculated using Equation Equation 10-48.

Equation 10-47.

where:

  • CP = correction for plunging flow
  • h = vertical distance of plunging flow from the center of the outlet pipe (ft. or m)
  • Do = outlet pipe diameter (ft. or m)
  • d = water depth in the manhole (ft. or m).

This correction factor corresponds to the effect of another inflow pipe plunging into the manhole on the inflow pipe for which the head loss is being calculated. Using the notations in Figure 10‑21, for example, calculate Cp for pipe number 2 when pipe number 1 discharges plunging flow. Consider the plunging flow that results from flow entering through the inlet into the manhole in the same manner. Only apply the correction factor when h is greater than d.

The table below presents correction factors for benching, CB. Benching refers to how the conduit is placed with respect to the manhole as follows:

  • Depressed floor -- The manhole bottom is lower than the storm drain conduit.
  • Flat floor -- The manhole bottom is flush with the storm drain conduit.
  • Half bench -- The bottom of the manhole is grouted or shaped to match up with the bottom half of the conduit.
  • Full bench -- The bottom of the manhole is grouted or shaped to the top of the storm drain conduit.
Anchor: #i1010924Correction Factor for Benching

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Correction Factor, CB

Bench Type

Pressure Flow

(d/DO > 3.2)*

Free Surface Flow

(d/DO < 1.0)*

Flat or Depressed Floor

1.0

1.0

Half Bench

0.95

0.15

Full Bench

0.75

0.07

* If 1.0 < d/DO < 3.2, use linear interpolation between pressure flow and free surface flow coefficients.



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