Determining normal depth
Normal depth calculation is one of the most commonly used analyses in stream restoration assessment and design. Several spreadsheets, computer programs, and nomographs are available for use in calculating normal depth. In a natural channel, with a nonuniform cross section, reliability of the normal depth calculation is directly related to the reliability of the input data. Sound engineering judgment is required in the selection of a representative cross section. The cross section should be located in a uniform reach where flow is essentially parallel to the bank line (no reverse flow or eddies). This typically occurs at a crossing or riffle.
Determination of the average energy slope can be difficult. If the channel cross section and roughness are relatively uniform, surface slope can be used. Thalweg slopes and low-flow water surface slopes may not be representative of the energy slope at design flows. Slope estimates should be made over a significant length of the stream (a meander wavelength or 20 channel widths). Hydraulic roughness is estimated based on field observations and measurements.
In addition to normal depth for a given discharge, these same procedures may be used to estimate average velocities in the cross section. These calculations do not account for backwater in a channel reach. The following example calculation refers to the cross section shown in figure 3.
Example problem: Normal depth rating curve calculation
Problem 1: Calculate a normal depth rating curve for each foot of depth up to 5 feet. Assume channel slope = 0.0015 and an n value = 0.03
Solution:
For
the value
Solving for Q, then:
Problem 2: Determine the normal depth for a discharge of 350 cubic feet per second and the associated average velocity.
Solution: From the rating curve calculated above, the 350 cubic feet per second discharge in this problem will be between Q3 and Q4. A straight-line interpolation gives a depth of 3.4 feet.
For velocity, since Q = VA
Discussion: The more complicated a section becomes, the more tedious is this hand calculation. Numerous computer programs, such as HEC–RAS (USACE 2001b), can perform normal depth calculations for a cross section of many coordinate points. A typical image from HEC–RAS is shown as figure 4.
