BASIC HYDRAULIC PRINCIPLES OF OPEN-CHANNEL FLOW

1 BASIC HYDRAULIC PRINCIPLES OF OPEN-CHANNEL FLOWBy Harvey E. Jobson and David C. GEOLOGICAL SURVEY open -File Report 88-707 Reston, Virginia 1988 DEPARTMENT OF THE INTERIOR DONALD PAUL HODEL, GEOLOGICAL SURVEY Dallas L. Peck, DirectorFor additional information write to:Chief, Office of Surface Water Geological Survey 415 National Center 12201 Sunrise Valley Drive Reston, Virginia 22092 Copies of this report can be purchased Geological Survey, Books and open -File Reports Box 25425, Federal Center Denver, Colorado 80225 CONTENTSPageAbstract.

2 1 introduction .. 1 Part I - BASIC PRINCIPLES of hydraulics for an ideal fluid .. 2 Lesson 1 - Fluid properties .. 2 Lesson 2 - Forces on submerged objects .. 8 Lesson 3 - Similitude and dimensional analysis .. 17 Lesson 4 - The energy equation for an ideal fluid .. 27 Part II - Steady uniform flow of real fluids in open channels .. 34 Lesson 5 - Velocity profiles .. 34 Lesson 6 - The energy equation applied to real fluids .. 43 Lesson 7 - Flow resistance .. 51 Lesson 8 - Computations for steady, uniform flow.

3 58 Part III - Advanced PRINCIPLES of steady flow .. 61 Lesson 9 - Flow in channel sections with variable roughness .. 61 Lesson 10 - The momentum principle .. 66 Lesson 11 - Specific energy .. 71 Part IV - Gradually varied flow in open channels .. 79 Lesson 12 - Determination of flow resistance in open channels .. 79 Lesson 13 - Classification of water-surface profiles .. 97 Lesson 14* - Local energy losses in natural channels .. 104 Lesson 15 - Water-surface profile computations .. 107 Part V - Discharge computations for rapidly varied flow.

4 116 Lesson 16 - Rapidly varied flow at constrictions .. 116 Lesson 17 - Flow through culverts .. 124 Lesson 18 - Flow over weirs .. 132 References .. 145 Answers to problems .. 147 ILLUSTRATIONSPageFigure 1-1. Free body diagram of fluid element .. 32-1. Definition sketch of the pressure prism for verticalrectangular gate .. 82-2. Definition sketch of the pressure prism for a submergedgate 4 feet wide .. 92-3. Definition sketch of the pressure prism to compute thetotal force of the water on a 4-foot wide gate .. 103-1.

5 Diagram illustrating flow through constriction, model, andprototype .. 174-1. Definition sketch of steady flow through a streamtube .. 284-2. Definition sketch for the flow of an ideal fluid in an openchannel .. 284-3. Definition sketch for the example problem of flow down aramp .. 305-1. Definition sketch for sheet flow over a wide inclined planeof width W .. 355-2. Diagram illustrating velocity distribution in a fullydeveloped, rough turbulent flow .. 38111 ILLUSTRATIONSPageFigure 6-1. Definition sketch of the energy diagram for open -channelflow.

6 436-2. Diagram illustrating typical flow through a bridgeconstriction .. 457-1. Diagram illustrating flow in a prismatic open channel .. 519-1. Definition sketch for cross section with overbank flow .. 6110-1. Diagram illustrating the control volume for applying the conservation of momentum equation for the flow past a pier .. 6711-1. Definition sketch for the specific energy curve .. 7111-2. Diagram illustrating flow changes from subcritical tosupercritical .. 7311-3. Diagram illustrating critical flow at the outlet of a boxculvert.

7 7412-1. Diagram illustrating eight types of roughness found insand-bed channels .. 9312-2. Diagram illustrating the effect of size of bed material and Froude number on the bed form and Manning's n for a range of flow conditions with sands of and median diameter in an 8-foot wide flume .. 9412-3. Graph showing the relation of stream power and mediangrain size to the bed form .. 9513-1. Sketch illustrating gradually varied flow in an openchannel longitudinal scale greatly reduced .. 9713-2. Definition sketch of surface profiles of varied flow.

8 9914-1. Sketch illustrating the energy grade lines at a localobstruction .. 10415-1. Definition sketch for water-surface profile computation .. 10815-2. Graph showing the variation of friction slope withdistance along the channel .. 10916-1. Sketch illustrating the theoretical water-surface andenergy profiles through a contracted opening .. 11616-2. Sketch illustrating the streamlines for flow through asharp-edged opening .. 11916-3. Graph showing the coefficients for type 1 opening,vertical embankments, and vertical abutments.

9 12117-1. Definition sketch of culvert flow .. 12417-2. Diagram illustrating the classification of culvert flow .. 12517-3. Graph showing the base coefficient of discharge for types I, 2, and 3 flow in box culverts with square entrance mounted flush in vertical headwall .. 12718-1. Definition sketch for a contracted, sharp-crested weir .. 13218-2. Definition sketch for a broad-crested weir .. 13218-3. Graph showing the coefficients of discharge for fullwidth, broad-crested weirs with downstream slope = 1:1,and various upstream slopes.

10 13418-4. Definition sketch of a V-notch (triangular) sharp-crestedweir .. 13718-5. Definition sketch of a Cippoletti (trapezoidal)sharp-crested weir .. 13918-6. Diagram illustrating various other sharp-crested weirprofiles .. 139 IVTABLESPageTable 1-1. Mechanical properties of some fluids .. 46-1. Kinetic energy correction coefficients for naturalchannels .. 4412-1. Values of the Manning resistance coefficient .. 8612-2. Equations for resistance based on bed-material size .. 9112-3. Sediment grade scale .. 9215-1. Criteria used to select friction slope equation.