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Open Channel Flow         Flows Under Pressure (Closed Conduits, Pipes)        References

Open Channel Flow
The Manning Equation is the most commonly used equation to analyze open channel flows.  The Manning Equation is utilized in our open channel design calculations - Design of Circular Culverts, Design of Rectangular Channels, and Design of Trapezoidal Channels.   It is a semi-empirical equation for simulating water flows in channels and culverts where the water is open to the atmosphere, i.e. not flowing under pressure, and was first presented in 1889 by Robert Manning.  The channel can be any shape - circular, rectangular, triangular, etc.  The units in the Manning equation appear to be inconsistent; however, the value k has hidden units in it to make the equation consistent.  The Manning Equation was developed for uniform steady state flow.   Uniform means that the channel is prismatic.  Prismatic means the channel has constant dimensions (including depth) along its length.  Steady state means the flowrate, velocity, and everything else are constant with time.  In reality no flow can be uniform and steady.  However, for individual channel reaches (e.g. one mile of a 200 mile river) the assumptions may be fairly well achieved.  The Manning Equation is also used successfully to simulate "gradually varied flow" where the channel is not prismatic.  In this case, S is the slope of the energy grade line.  For prismatic flows, S is the slope of the hydraulic grade line which is the slope of the water surface and is the same as the slope of the channel bottom.

Flows Under Pressure (Closed Conduits, Pipes)                            To top of page
This website has two comprehensive calculations for simulating steady flows under pressure - Design of Circular Water Pipes and Design of Circular Liquid or Gas Pipes.  We also have a water hammer calculation that predicts pressures during transient conditions due to closing or opening a valve.  In addition, we have calculations for flow measurement using orifices, nozzles, and venturi meters.  The website also has several smaller calculations which solve individual portions of the energy equation; these smaller calculations are linked in the following paragraph.

The energy equation represents elevation, pressure, and velocity forms of energy.  The energy equation for a fluid moving in a closed conduit is written between two locations at a distance (length) L apart.  Energy losses for flow through ducts and pipes consist of major losses and minor losses.   Major losses are due to friction between the moving fluid and the inside walls of the duct.   Minor losses are due to fittings such as valves and elbows.  Major losses are computed using either the Darcy-Weisbach friction loss equation (which utilizes the Moody friction factor) or the Hazen-Williams friction loss equation.  The Darcy-Weisbach method is generally considered more accurate than the Hazen-Williams method.   Additionally, the Darcy-Weisbach method is valid for any liquid or gas; Hazen-Williams is only valid for water at ordinary temperatures (40 to 75 ^oF).  The Hazen-Williams method is very popular, especially among civil engineers, since its friction coefficient (C) is not a function of velocity or duct (pipe) diameter.  Hazen-Williams is simpler than Darcy-Weisbach for calculations where you are solving for flowrate, velocity, or diameter.

References                                    To top of page
   For open channel flow:
Chaudhry, M. H.  1993.  Open-Channel Flow.  Prentice-Hall, Inc.

Chow, V. T.  1959.  Open-Channel Hydraulics.  McGraw-Hill, Inc. (the classic text)

French, R. H.  1985.  Open-Channel Hydraulics.  McGraw-Hill Book Co.

Mays, L. W. editor.  1999.  Hydraulic design handbook.  McGraw-Hill Book Co.

Munson, B.R., D. F. Young, and T. H. Okiishi.  1998.  Fundamentals of Fluid Mechanics.  John Wiley and Sons, Inc.  3ed.

Streeter, V. L., E. B. Wylie, and K. W. Bedford.  1998.  WCB/McGraw-Hill. 9ed.

    For closed conduit flow:
Munson, B.R., D. F. Young, and T. H. Okiishi.  1998.  Fundamentals of Fluid Mechanics.  John Wiley and Sons, Inc.  3ed.

Gerhart, P. M, R. J. Gross, and J. I. Hochstein.  1992.  Fundamentals of Fluid Mechanics.  Addison-Wesly Pubishing Co.  2ed.

Hwang, N. H. C. and R. J. Houghtalen.  1996.  Fundamentals of Hydraulic Engineering Systems.  Prentice Hall.  3ed.

Mays, L. W. editor.  1999.  Hydraulic design handbook.  McGraw-Hill Book Co.

Potter, M. C. and D. C. Wiggert.  1991.  Mechanics of Fluids.   Prentice-Hall, Inc.

Roberson, J. A., J. J. Cassidy, and M. H. Chaudhry.  1998.  Hydraulic Engineering.  John Wiley and Sons, Inc.  2ed.

Roberson, J. A. and C. T. Crowe.  1990.  Engineering Fluid Mechanics.   Houghton Mifflin Co.

Streeter, V. L., E. B. Wylie, and K. W. Bedford.  1998.  WCB/McGraw-Hill. 8ed.

White, F. M.  1979.  Fluid Mechanics.  McGraw-Hill, Inc.

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