The Excel template shown at the right can be used to calculate the volumetric flow rate, Q, and flow velocity, V,įor specified values of D, nfull, and S for a partially full pipe that is flowing more than half full. n/nfull = 1.29 - (y/D - 0.3)(0.2) for 0.3 The equations to calculate n/nfull, in terms of y/D for y < D/2 are as follows The equations that apply to this case of flow depth less than pipe radius, as used in the Excel formulas in the spreadsheet template are as follows (along with the Manning equation and Q = VA ): K is the circular segment area h is the circular segment height S is the circular segment arc length θ is the central angle, and r is the radius of the pipe. The diagram at the right shows the parameters used in partially full pipe flow calculations when the flow depth is less than the pipe radius. The Excel template shown at the left can be used to calculate the volumetric flow rate, Q, and flow velocity, V,įor specified pipe diameter, D flow depth, y Manning roughness for full pipe flow, nfull and bottom slope, S, for a partially full pipe that is flowing less than half full. Excel Template for Calculation of Q and V with Pipe Less Than Half Full Go to page 2 for discussion of Excel spreadsheet templates and the equations used in them for calculating Q and V in partially full pipe flow. The equations and spreadsheets presented and discussed in this article use the variation in n that was developed by T.R. If you are making partially full pipe flow calculations, you should be aware that there are online calculators and websites with equations for making partially full pipe flow calculations using the Manning equation with constant Manning roughness coefficient, n. For partially full pipe flow, however, use of the variation in Manning roughness coefficient, developed by Camp and shown in the diagram above, gives better agreement with experimental measurements. It was developed for, and is widely used with great success for, flow in rectangular and trapezoidal channels using a constant value for the Manning roughness coefficient, n. It is well to keep in mind, however, that the Manning equation is an empirical equation. Intuitively, one would not expect the Manning roughness coefficient to change due to a change in depth of flow in a pipe. Camps method consisted of using a variation in Manning roughness coefficient with depth of flow as shown in the graph in the preceding section. Camp developed a method for improving the agreement of partially full pipe flow calculations with measured values and presented it in a 1946 journal article (ref #2). By the mid twentieth century it had been observed that measured flow rates in partially full pipe flow don’t agree with those calculated as just described. Unfortunately there is a flaw in this procedure. 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. The cross-sectional area, wetted perimeter, and hydraulic radius for partially full pipe flow can be calculated for given pipe diameter and depth of flow with the geometric/trigonometric equations that are discussed in the next couple of sections. The Manning Roughness Coefficient and Partially Full Pipe Flow 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. Qfull and Vfull can be readily calculated from the Manning equation, because the hydraulic radius for a circular pipe flowing full is simply D/4.Įxcel formulas, however, make use of the rather inconvenient equations for partially full pipe flow easy to use. Q and V are the flow rate and velocity with depth of flow y in a pipe of diameter D. This has led to the use of graphs of Q/Qfull and V/Vfull vs y/D, like the one shown at the left. As a result there is no relatively simple equation for hydraulic radius in terms of flow depth and pipe diameter. With the use of the Manning equation, however, is the complicated nature of the equations for area of flow and wetted perimeter for partially full pipe flow. For background on the Manning Equation, see the article, “ Introduction to the Manning Equation for Uniform Open Channel Flow Calculations.” A difficulty Partially full pipe flow under gravity is an example of open channel flow, so the Manning equation applies if it is uniform flow. History of the Liberty Ships from World War 2: The Fatally Flawed Ships
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