Critical Depth in Circular Pipe (Culvert) Calculation |
Critical depth is a function of the flow rate and pipe diameter |
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Register to enable "Calculate" button. Critical depth calculation is mobile-device-friendly as of October 30, 2013. Units in critical depth calculation: cm=centimeter, ft=feet, gal=US gallons, m=meters, min=minute, s=second Introduction 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. Equations 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 θ_{c} and then for Y_{c}.
Notation "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
diameter. © 2009-2013 LMNO Engineering, Research, and Software, Ltd. (All Rights Reserved) LMNO Engineering, Research, and Software, Ltd. August 19, 2015: Made text fields narrower to show 8 significant figures rather than 16. Calculation still uses double precision internally. |
To: LMNO Engineering home page (more calculations) Related calculations: Manning Equation for Circular Culvert Culvert Design using Inlet and Outlet Control Flowrate using End Depth Method |