Manning–Chezy Calculator
Enter Manning roughness n and hydraulic radius R to compute the Chezy coefficient C = R^(1/6)/n.
Input Data
Results
At a glance:The Chezy coefficient C appears in the Chezy equation for uniform open-channel velocity: v = C·√(R·S), with R the hydraulic radius and S the slope. Manning's equation gives v = (1/n)·R^(2/3)·S^(1/2). Equating the two yields the Manning–Chezy relation C = R^(1/6)/n (with C in SI units, m^(1/2)/s). Thus a rougher channel (larger n) lowers C, and a larger hydraulic radius raises C (but only as R^(1/6)). This conversion lets you switch between the two classic formulas. This tool computes C = R^(1/6)/n from R and n.
Formula
Chezy: v = C·√(R·S)
Manning–Chezy: C = R^(1/6)/n
$$C = \dfrac{R^{1/6}}{n}$$How to Use
- Enter the hydraulic radius R (m).
- Enter Manning's n.
- The calculator returns the Chezy coefficient C.
Case Studies
Concrete channel
R = 0.5 m, n = 0.013.
C = 0.5^(1/6)/0.013 ≈ 53.6 m^½/s.
Matches typical concrete-lined channel value.
FAQ
When would I use Chezy vs Manning?
They are interchangeable for uniform flow; Manning's n is more common in practice (easier to tabulate). C depends on both n and R via C = R^(1/6)/n.
Why R^(1/6)?
It comes from matching Manning's R^(2/3) to Chezy's R^(1/2): (1/n)·R^(2/3) = C·R^(1/2) → C = R^(1/6)/n.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.