Harlan Bengtson (Author of Advantages of Spreadsheets for Pipe Flow/Friction Factor Calculations)
Physics Fluid Flow (1 of 7) Bernoulli's Equation
Using Spreadsheets for Calculating Partially Full Pipe Flow
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Bengtson, PhD, P. Continuing Education and Development, Inc. IntroductionThe Manning equation can be used for uniform flow in a pipe, but the Manningroughness coefficient needs to be considered to be variable, dependent upon thedepth of flow. This course includes a review of the Manning equation, along withpresentation of equations for calculating the cross-sectional area, wetted perimeter,and hydraulic radius for flow of a specified depth in a pipe of known diameter. Equations are also given for calculating the Manning roughness coefficient, n, for agiven depth of flow in a pipe of known diameter.
Relationship to the Chezy Coefficient
As a result there is no relatively simple equation for hydraulic radius in terms of flow depth and pipe diameter. Q and V are the flow rate and velocity with depth of flow y in a pipe of diameter D. Excel formulas, however, make use of the rather inconvenient equations for partially full pipe flow easy to use. Four downloadable Excel spreadsheet templates for making different types of partially full pipe flow calculations are presented and discussed in the rest of this article. If the pipe slope and Manning roughness coefficient are known, then the Manning equation can be conveniently used to calculate flow rate and velocity for the given depth of flow.
In fluid mechanics, flows in closed conduits are usually encountered in places such as drains and sewers where the liquid flows continuously in the closed channel and the channel is filled only up to a certain depth. Closed conduit flow differs from open channel flow only in the fact that in closed channel flow there is a closing top width while open channels have one side exposed to its immediate surroundings. Closed channel flows are generally governed by the principles of channel flow as the liquid flowing possesses free surface inside the conduit. Consider a closed circular conduit of diameter D, partly full with liquid flowing inside it. Therefore, the hydraulic radius R h is calculated using cross-sectional area A and wetted perimeter P using the relation:. In practice, it is common to restrict the flow below the value of 0.