Other Properties of ZnO NWs

A studyʹs limits or boundaries are usually different from those of the detailed studyʹs hydraulic computations. The final inundation mapping may cover only the city limits or local political boundary. For accurate flood elevations at the political boundary or location of interest, however, water surface profile analyses must begin well down-stream of the boundary. Similarly, if a new bridge or flood reduction measure, such as a reservoir or levee, is proposed, the hydraulic analysis must evaluate how far any adverse effects extend upstream. Depending on the stream slope, the downstream boundary for beginning the hydraulic computations may be a mile (1.6 km) or more past the study boundary. Upstream, the effects of an obstruction could extend several times this distance from the obstruction. These effects can also extend up tributaries that are significantly affected by backwater from the main river.

Downstream Hydraulic Boundary. Chapter 2 states that a stream flows at or near normal depth if the channel is prismatic and the slope is constant. A natural river always has geometry and slope that vary from location to location; however, the river will still trend toward normal depth. An obstruction or drop-off in the channel bed may cause a significant change to the water surface elevation at its location, but the

Section 5.2 Study Limits and Boundary Determinations 115

water surface elevations in the river will taper back toward normal depth as the effects of the obstruction damp out with distance.

Water surface profile calculations require a starting water surface elevation. The downstream boundary defines the starting water surface elevation for subcritical flow, while the upstream boundary defines the starting water surface elevation for supercritical flow. For subcritical flow, the downstream hydraulic boundary should be located such that any errors in the starting water surface elevation will be damped out before the start of the detailed hydraulic study reach. In the past, determining this location was simply guesswork, with computations for a selected discharge starting at critical depth and at one or two other elevations above and below the estimated nor-mal depth. Engineers then reviewed their computations to determine whether all the profiles converged to the same value before the start of the reach under study, as shown in Figure 5.1.

The USACE’s Hydrologic Engineering Center published Accuracy of Computed Water Surface Profiles (USACE, 1986) one of the few definitive guides for determining where to locate this boundary. Their work, prepared for the U.S. Federal Highway Adminis-tration, developed a prediction equation and nomograph for locating the downstream hydraulic boundary. Figures 5.2 and 5.3 show the nomographs for starting conditions of critical and normal depth, respectively.

The equation for downstream reach length for the critical depth criterion in Figure 5.2 is

(5.1) where L_DC = the downstream reach length for computations starting at critical

depth (ft)

HD = the average hydraulic depth for the reach (1% chance flow) (ft) S = the average reach slope (ft/mi)

The equation for downstream reach length for the normal depth criterion in Figure 5.3 is

U.S. Army Corps of Engineers

Figure 5.1 Study distance analysis concepts.

L_DC 6600HD ---S

=

(5.2) where L_DN = the downstream reach length for computations starting at normal

depth (ft)

If the engineer can estimate the river slope (from a topographic map) and the hydrau-lic depth (possibly from assuming normal depth for the computation) for the 100-year flood event, the nomograph can be used to determine how far downstream from the beginning of the detailed study to begin computations for both normal and critical depth. Although it may be difficult to determine the hydraulic depth alone, HEC-RAS does compute and show hydraulic depth for each cross section. After data entry and an initial run, the output can be reviewed for the calculated hydraulic depths. These results can then be used in Equations 5.1 and 5.2 or the nomographs of Figures 5.2 and 5.3 to reestablish the proper start of computations.

U.S. Army Corps of Engineers

Figure 5.2 Downstream reach-length estimation – critical depth criterion.

L_DN 8000HD^0.8 ---S

=

Section 5.2 Study Limits and Boundary Determinations 117

Example 5.1 Computing the location of the downstream hydraulic study boundary.

A reach of stream to be modeled with HEC-RAS has an average slope of 10 ft/mi, esti-mated from a topographic contour map. Based on the engineerʹs judgement, the initial estimate of the reachʹs average hydraulic depth (cross-section area/top width) for the 100-year flood profile is 8.0 feet. Estimate the location of the downstream boundary (first cross section) so that profiles will converge before the beginning of the detailed study boundary.

For boundary conditions starting with critical depth, Equation 5.1 gives

For boundary conditions starting with normal depth, Equation 5.2 gives

U.S. Army Corps of Engineers

Figure 5.3 Downstream reach length estimation – normal depth criterion.

L_DC 6600HD

---S 66008

10--- 5280 ft

= = =

These distances may be used for an initial location of the boundary. Additional cross sections should be included between the hydraulic boundary and the beginning of the detailed study boundary. HEC-RAS should then be used to solve for hydraulic depth.

If the computed hydraulic depth is significantly different from the initial estimate, the L_DC and L_DN values should be recomputed and the distances adjusted in the model. If the engineer wants to use both normal and critical depths at the boundary, thereby performing multiple computer runs, the longer distance should be selected for use in the model.

Example 5.2 Computing the location of the downstream hydraulic study boundary.

Compute the same distances for Example 5.1, assuming the average stream slope is 2 ft/mi.

For boundary conditions starting with critical depth, Equation 5.1 gives

For boundary conditions starting with normal depth, Equation 5.2 gives

For flatter streams, the downstream reach distances are significant. Very mildly slop-ing streams may require a reach of several miles before the profile converges.

Upstream Hydraulic Boundary and Project Effects. The upstream hydraulic boundary is normally the location along the stream where no further hydraulic com-putations are needed. For a flood insurance study, this location is usually the upstream corporate limits of the municipality. For a flood protection project, the effects extend upstream for some distance past the end of the project. Part of the hydraulic analysis is to determine how far this effect extends and to identify and miti-gate any adverse effects caused by the project. This is accomplished by creating two HEC-RAS simulations, one with and one without the project, then locating where the two profiles converge upstream. HEC’s Accuracy of Computer Water Surface Profiles (USACE, 1986) suggests using a prediction equation and nomograph for locating the upstream limit for project effects under subcritical conditions. This location is defined as the point where there is no more than 0.1 ft (0.03 m) between the water surface pro-files computed with and without the obstruction. The work done by HEC specifically addressed the effects of a bridge; however, it could be used for estimating the distance for levee effects or for small weirs or check dams. Figure 5.4 shows the nomograph for upstream estimation with subcritical flow.

The equation for calculating the upstream reach is

(5.3)

Section 5.2 Study Limits and Boundary Determinations 119

where L_U = the upstream reach length (ft)

HD = the average hydraulic depth (100-year event flow) (ft)

HL = the head loss at the channel crossing structure for the 100-year flow (ft) S = the average reach slope

Estimating the upstream limit requires a third variable: the head loss at the obstruc-tion, or the difference in water surface elevation just upstream of the bridge with and without bridge conditions. If a proposed bridge or other obstruction will result in an effect beyond the upper end of the study reach, Figure 5.4 may be used to determine how far beyond the nominal study limits the profile computations should extend.

In some cases, a supercritical flow profile is necessary. For this flow regime, the start-ing water surface elevation is specified at the upstream hydraulic boundary (upstream from the detailed study boundary), because supercritical flow computa-tions proceed in the downstream direction. There is no formal guidance on how far the hydraulic boundary should be located upstream of the detailed study boundary

U.S. Army Corps of Engineers

Figure 5.4 Upstream reach-length estimation for subcritical flow.

for supercritical flow conditions. However, unless the computations are strictly for a supercritical flow (man-made) channel, the resulting profile may well be a mix of sub-critical and supersub-critical flow stream reaches. (This mixed-flow analysis is discussed in Chapters 8 and 11.)

Example 5.3 Computing the upstream effect of an obstruction.

Assume that the same reach of stream in Example 5.1 has a bridge causing an esti-mated 2 ft of water surface increase (swellhead) for the 100-year event. How far upstream will the effect of the bridge extend?

From Example 5.1, the estimated hydraulic depth is 8 ft and the stream slope is 10 ft/mi. To estimate the upstream effect of a bridge obstruction, Equation 5.3 gives

Example 5.4 Computing the upstream effect of an obstruction.

Assume that the reach of stream from Example 5.2 has a bridge causing an estimated 2 ft of swellhead for the 100-year event. How far upstream will the effect of this bridge extend?

The stream slope of Example 5.2 is 2 ft/mi. Equation 5.3 is still appropriate and gives

Comparing the results of Example 5.3 and Example 5.4 shows that the milder the slope, the farther upstream the effects of the obstruction extend.