Steady versus unsteady flow

Many hydraulic parameters of interest in typical designs and assessment can be calculated by assuming a normal depth. Normal depth calculations are often based on a solution to Manning’s equation. This approach is relatively simple, but only applicable in uniform flow conditions where the gravitational forces are exactly offset by the resistance forces. Manning’s equation is an infinite slope model that assumes mean depth, velocity, and area are the same from cross section to cross section. It can only occur in long, straight, prismatic channels where the terminal velocity of the flow is achieved. This assumption cannot account for backwater conditions nor variable channel shape, roughness, and slope. Natural channels approach, but rarely achieve uniform, normal depth. Designs and assessments that depend on calculations based on normal depth must consider the affects of possible errors.

Even though flows in a stream are readily observable at any time, they are unsteady at every spatial and temporal scale. Typically, unsteady modeling results in variations in flow rate, velocity, and depth in space and time throughout the modeled reach. In most unsteady flow models, the discharges can vary within a model, and the boundary conditions are in terms of flow and stage with time. Unsteady flow calculations are often used to analyze a dam breach, inchannel storage, variable boundary conditions, rapidly rising hydrographs on flat slopes, irrigation withdrawals, tributary flow interaction, and locations where duration of flooding is an issue.

Unsteady flow models can be contrasted to steady flow models with no time component in the calculations. Steady flow models are typically much simpler to calibrate and execute than unsteady flow models. For most steady flow models, the depth and velocity may change from section to section, but only one flow is allowed per section per model run. Since the flow is constant with respect to time, only one discharge is calculated for each section in a given steady flow model run. In addition, boundary conditions are held constant. These assumptions are often suitable for many analyses where the reach is short or the primary interest is an assessment of the peak hydraulic parameters for a given discharge.

In alluvial channels, the interaction of sediment with the flow can also have a profound affect since the amount and type of sediment load affects the energy balance of the flow. Equations of sediment motion (sediment continuity and sediment transport) are covered in NEH654.13.