Here’s a comprehensive table summarizing the key aspects of Manning’s Equation for pipe flow:
Aspect
Details
Equation
v=1nR2/3S1/2v=n1R2/3S1/2
Variables
v = velocity of fluid flow (m/s or ft/s) n = Manning’s roughness coefficient R = hydraulic radius (m or ft) S = slope of energy grade line (m/m or ft/ft)
Flow Rate Formula
Q=A⋅v=AnR2/3S1/2Q=A⋅v=nAR2/3S1/2
Application
Open channels and partially filled pipes
Limitations
– Relative roughness (R/k) between 7 and 130 – Fully turbulent flow – Not recommended for storm drainage pipes
Hydraulic Radius (R)
For circular pipes running full: R = diameter/4
Manning’s n
Empirically derived coefficient based on surface roughness and sinuosity
Full vs. Partial Flow
Qfull is less than Q at 94% depth due to increased friction
Practical Use
Sizing pipes, calculating flow capacity, and estimating velocities
Advantages
Simple to use, widely accepted in civil engineering
Disadvantages
Empirically derived, less accurate than Colebrook-White equation for certain conditions
Historical Note
Developed by Philippe Gaspard Gauckler (1867) and Robert Manning (1890)
Alternative Names
Gauckler–Manning formula, Gauckler–Manning–Strickler formula
This table provides a concise overview of Manning’s Equation for pipe flow, including its formula, key variables, applications, limitations, and practical considerations.