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D5388-21 – Standard Test Method Technical Guide
📐 Channel Geometry and Cross-Section Requirements
ASTM D5388-21 provides a standard test method for computing the discharge of water in open channels using the step-backwater method. This computation relies heavily on precisely defined cross-sectional characteristics. Cross sections are numbered consecutively in the downstream order and must be positioned as nearly as possible at right angles to the direction of flow. Each section requires a detailed definition using coordinates of horizontal distance and ground elevation to accurately represent the channel geometry.
The primary geometric features are the cross-section area (A) and the wetted perimeter. The cross-section area (A) is defined as the area below the water-surface elevation being analyzed, calculated as the summation of the products of mean depth multiplied by the width between survey stations. Conveyance (K), which measures the carrying capacity of a channel without regard to slope, has dimensions of cubic feet per second and is a foundational element of the step-backwater computation.
| 🟦 Parameter | 📏 Symbol | 📐 Definition / Formula | 🎯 Standard Unit | ⚡ Notes |
|---|---|---|---|---|
| Conveyance | K | K = (1.49 / n) A R2/3 | ft³/s | Key measure of channel capacity |
| Velocity-head Coeff. | α | α = Σ(ki³ ai²) / (KT³ AT²) | Dimensionless | Unity if section is unsubdivided |
| Cross-section Area | A | A = Σ (Mean Depth × Width) | ft² | Computed for a specific stage |
| Discharge (Indirect) | Q | Iteratively solved via energy eq. | ft³/s | Defines point on stage-discharge rating |
⚙️ Computational Procedure and Governing Equations
The step-backwater method performs gradually-varied flow computations moving in an upstream direction. Starting from a known water-surface elevation at a downstream control section, the computation proceeds section by section. The standard requires the water-surface elevation of the upstream-most cross section and coefficients of channel roughness (Manning’s n) as input. The assumed discharge is iteratively adjusted until the computed water-surface profile matches the observed conditions, typically high-water marks from a single flood event.
💡 Best Practice for Convergence: When adjusting the assumed discharge, ensure the velocity-head coefficient (α) is recalculated if the subdivision of the cross section changes. For unsubdivided sections, α is assumed equal to unity, significantly simplifying the energy balance.
The standard mandates that the values stated in inch-pound units are regarded as standard, with SI unit conversions provided for information only. The following table illustrates the typical data structure required for a surveyed cross section within the computational model:
| 📌 Station (ft) | 📐 Ground Elev. (ft) | 🟦 Manning’s n | ⚡ Conveyance (K) |
|---|---|---|---|
| 0.0 | 102.50 | 0.045 | — |
| 15.0 | 100.00 | 0.035 | Computed per subsection |
| 30.0 | 101.80 | 0.040 | — |
| Water Surface Elev. (Upstream): 105.2 ft | Roughness Source: Barnes (1967) | |||
📊 Key Measured Parameters and Channel Roughness
The accuracy of the computed discharge is heavily dependent on the selection of Manning’s n roughness coefficients. This test method is intended as an indirect measurement for a single flow event, usually a specific flood, to define a point on the stage-discharge relation. The standard references test methods D3858 (Velocity-Area Method) and D2777 for related precision and bias practices, but ultimately D5388 relies on hydraulic engineering judgment to select roughness values.
⚠️ Critical Input Sensitivity: The roughness coefficient (Manning’s n) is a highly sensitive parameter in the conveyance equation (K = 1.49/n A R2/3). Users must reference established guides for natural channels (e.g., Barnes, “Roughness Characteristics of Natural Channels”) to ensure defensible discharge results.
The dimensionless velocity-head coefficient (α) represents the ratio of the true velocity head to the velocity head computed on the basis of mean velocity. Using the correct α value is essential for modeling energy losses, especially in complex, subdivided channels where the flow distribution is highly uneven.
❓ Frequently Asked Questions
🔍 What is the primary purpose of the Step-Backwater Method (D5388)?
To compute an indirect measurement of discharge for a single flow event in open channels or streams. The computed discharge is typically used to define a specific point on the stage-discharge rating curve for a gauging station.
💡 How is the velocity-head coefficient (α) determined?
Alpha is assumed equal to unity if the cross section is not subdivided. For subdivided sections, it must be computed using the formula α = Σ(ki³ ai²) / (KT³ AT²), where k and a are the conveyance and area of each subsection.
⚡ What units are standard for this test method?
The values stated in inch-pound units (feet, square feet, cubic feet per second) are regarded as standard. Conversions to SI units are provided in the standard for informational purposes only.
📌 What are the essential input data required by D5388?
The computation requires representative cross-sectional coordinates (station and elevation), the water-surface elevation of the upstream-most cross section, and coefficients of channel roughness (Manning’s n) applied to the channel and overbank areas.