Determining the water surface in curved channels
Water surface profiles as computed by HEC–RAS assume a level water surface in each cross section. This is not the case in a curved channel. However, the water surface calculated by HEC–RAS is valid along the centerline of the flow. Generally, HEC–RAS can account for the friction and eddy losses caused by a bend so that the water surface computed upstream would be correct. However, the super-elevated water surface in the bend itself must be calculated separately. The following formula is often used for estimating super-elevation in a water surface.
where:
V = average channel velocity (ft/s)
b = channel top width (ft)
g = gravitational acceleration (32.2 ft/s2)
rc = radius of curvature of the channel (ft)
ΔZ = super-elevation in ft from bank to bank, so the amount added to or subtracted from the centerline elevation would be half that. A factor of safety of 1.15 is generally applied.
In supercritical flow, curved channels are much more complicated due to wave patterns that propagate back and forth across the channel and downstream. With the disturbances reflecting from one side to the other, higher water surfaces can occur both on the inside and outside banks of a bend. Although a methodology for determining the super-elevation is developed by Chow (1959) for a regular curved channel with a constant width, it also approximates that for a natural channel.
Example problem: Super-elevation
Problem: A trapezoidal channel has a 30-foot bottom width, 1H:3V side slopes, and a radius of 100 feet. For a 500 cubic feet per second discharge, the depth is 4.12 feet, and the cross-sectional area is 174.5 square feet. Find the increase in water surface on the outside of the curve.
Solution: Calculate the velocity, from Q = VA:
top width is:
so, the increase in the flow depth on the outside of the curve is 0.07 feet, which is half of 0.14 feet.