Manning Formula

The Manning formula is an empirical formula estimating the average velocity of a liquid flowing in a conduit that does not completely enclose the liquid, such as open-channel flow.

The flow velocity of the fluid increases with the square root of the hydraulic grade line slope and the flow area to the two-thirds power. It decreases inversely with the wetted perimeter to the two-thirds power and the Manning's roughness coefficient. The flow rate equals the flow area times the flow velocity of the fluid.

Formula

${QuantityVariable["v", "Speed"] == (Quantity[1, "Meters"^(1/3)/"Seconds"]*(QuantityVariable["A", "Area"]/QuantityVariable["P", "Length"])^(2/3)*Sqrt[QuantityVariable["S", "Unitless"]])/QuantityVariable["n", "ManningRoughnessCoefficient"], QuantityVariable["Q", "VolumeFlow"] == QuantityVariable["A", "Area"]*QuantityVariable["v", "Speed"]}$

symbol	description	physical quantity
v	flow velocity of fluid	"Speed"
n	Manning's roughness coefficient	"ManningRoughnessCoefficient"
A	flow area	"Area"
P	wetted perimeter	"Length"
S	hydraulic grade line slope	"Unitless"
Q	flow rate	"VolumeFlow"

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$FormulaData[ ResourceObject[ "Manning Formula"], {QuantityVariable["P","Length"] -> Quantity[9.5`, "Meters"], QuantityVariable["Q","VolumeFlow"] -> Quantity[1218.12`, ("Meters")^3/("Seconds")], QuantityVariable["A","Area"] -> Quantity[202.5`, ("Meters")^2], QuantityVariable["n","ManningRoughnessCoefficient"] -> 0.014`}]$

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Manning Formula

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