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## Applying the Momentum Equation to Determine Water Depth between Bridge Piers  1-Newbie

## Applying the Momentum Equation to Determine Water Depth between Bridge Piers

created by By D.M. Griffin, Jr. • Calculate the water depth between bridge piers and the depth of flow so that the flow regime remains subcritical
• Apply in Hydraulics, Mechanical Engineering, and Civil Engineering
• Perform using depth, drag, depth of flow, drag coefficient, weight of water, velocity, water density, flow rate, Froude number, hydrostatic forces, subcritical and supercritical flow regime, plots, etc.

This worksheet shows the application of the momentum equation to determine the water depth between bridge piers. For this problem, the pier width, upstream depth of the river and velocity, and the drag coefficient of the piers are given. The worksheet shows you how to find the depth of flow downstream of the bridge piers so that the flow regime remains subcritical.

To begin, the worksheet lays out all of the relevant factors and begins by calculating the drag coefficient. It then shows you how to define a control volume. In this instance you use the volume bounded by the channel and dotted lines. It then shows you how to re-write the momentum function in a different form so that it is easy to plot. The line will cross the x axis twice- implying the subcritical flow regime and the supercritical flow regime. The worksheet then shows you how you might analyze the plot in accordance with HEC-RAS.

All notation, images, plots, formulas, equations, and solutions are provided to aid you in your own calculations. 