Standard Step Method

The Standard Step Method (STM) is a computational technique utilized to estimate one-dimensional surface water profiles in open channels with gradually varied flow under steady state conditions. It uses a combination of the energy, momentum, and continuity equations to determine water depth with a given a friction slope ${\displaystyle (S_{f})}$, channel slope ${\displaystyle (S_{0})}$, channel geometry, and also a given flow rate. In practice, this technique is widely used through the computer program HEC-RAS, developed by the US Army Corps of Engineers Hydrologic Engineering Center (HEC).

The energy equation used for open channel flow computations is a simplification of the Bernoulli Equation (See Bernoulli Principle), which takes into account pressure head, elevation head, and velocity head. (Note, energy and head are synonymous in Fluid Dynamics. See Pressure head for more details.) In open channels, it is assumed that changes in atmospheric pressure are negligible, therefore the “pressure head” term used in Bernoulli’s Equation is eliminated. The resulting energy equation is shown below:

For a given flow rate and channel geometry, there is a relationship between flow depth and total energy. This is illustrated below in the plot of energy vs. flow depth, widely known as an E-y diagram. In this plot, the depth where the minimum energy occurs is known as the critical depth. Consequently, this depth corresponds to a Froude Number ${\displaystyle (F_{n})}$ of 1. Depths greater than critical depth are considered “subcritical” and have a Froude Number less than 1, while depths less than critical depth are considered supercritical and have Froude Numbers greater than 1. (For more information, see Dimensionless Specific Energy Diagrams for Open Channel Flow.)

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