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The Manning formula or Manning's equation is an empirical formula estimating the ... hydraulic head loss loss ... are only constant for a range of flow rates.
The head loss Δh (or h f) expresses the pressure loss due to friction in terms of the equivalent height of a column of the working fluid, so the pressure drop is =, where: Δh = The head loss due to pipe friction over the given length of pipe (SI units: m); [b]
h f = head loss in meters (water) over the length of pipe; L = length of pipe in meters; Q = volumetric flow rate, m 3 /s (cubic meters per second) C = pipe roughness coefficient; d = inside pipe diameter, m (meters) Note: pressure drop can be computed from head loss as h f × the unit weight of water (e.g., 9810 N/m 3 at 4 deg C)
Before being able to use the minor head losses in an equation, the losses in the system due to friction must also be calculated. Equation for friction losses: = [5] [3] [1] = Frictional head loss = Downstream velocity
The following table gives flow rate Q such that friction loss per unit length Δp / L (SI kg / m 2 / s 2) is 0.082, 0.245, and 0.816, respectively, for a variety of nominal duct sizes. The three values chosen for friction loss correspond to, in US units inch water column per 100 feet, 0.01, .03, and 0.1.
Given a starting node, we work our way around the loop in a clockwise fashion, as illustrated by Loop 1. We add up the head losses according to the Darcy–Weisbach equation for each pipe if Q is in the same direction as our loop like Q1, and subtract the head loss if the flow is in the reverse direction, like Q4.
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Since the Chézy formula and the Manning formula both reference a single control volume location along the channel, neither address friction factor nor head loss [7] directly. However, the change in pressure head may be calculated by combining them with other formulas such as the Darcy–Weisbach equation. [2]