Critical Depth in Circular Pipe (Culvert) Calculation
Critical depth is a function of the flow rate and pipe diameter
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Units in critical depth calculation: cm=centimeter, ft=feet, gal=US gallons, m=meters, min=minute, s=second
As water flows down a culvert, the depth may change and pass through the critical depth if the bottom slope, geometry, or pipe material changes. If the flow is initially subcritical and the channel slope increases, the water may undergo a hydraulic drop if it transitions from subcritical to supercritical. Conversely, if the flow is supercritical and the culvert slope becomes flatter, then there could be a hydraulic jump such that the water passes through the critical depth as it becomes subcritical.
The channel cross-sectional area can be written in terms of the geometry as (Chow, 1959, p. 21):
Critical depth occurs when energy is at a minimum with respect to depth, dE/dY=0. The following equation is obtained when energy is minimized:
LMNO Engineering uses a numerical solution method to solve the above equation for θc and then for Yc.
"Need larger Q or smaller D". Run-time error. The combination of flow rate and diameter that were input result in a very small critical depth approaching machine precision.
"Need smaller Q or larger D". Run-time error. The combination of
flow rate and diameter that were input result in critical depth greater than the pipe
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LMNO Engineering home page (more calculations)
Manning Equation for Circular Culvert
Culvert Design using Inlet and Outlet Control
Flowrate using End Depth Method
Hydraulic Jump in a Pipe or Culvert