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Flume Studies Using Medium Sand (0.45 Mm)

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Flume Studies Using Medium Sand (0.45 Mm) Flume Studies Using Medium Sand (0.45 mm) GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1498-A RECEIVED MAY 2 Flume Studies Using Medium Sand (0.45 mm) By D. B. SIMONS, E. V. RICHARDSON and M. L. ALBERTSON STUDIES OF FLOW IN ALLUVIAL CHANNELS GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1498-A A comprehensive study of fluvial hydraulics UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1961 UNITED STATES DEPARTMENT OF THE INTERIOR STEWART L. UDALL, Secretary GEOLOGICAL SURVEY Thomas B. Nolan, Director For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. CONTENTS Page Symbols and dimensions.-.-__________-_--_-_________-_______--__-__ vi Glossary of terms_______-____________________-_-_-____-___---__---_ vu Abstract__ ______________________________________________________ A-1 Introduction. _____________________________________________________ 1 History ______________________________________________________ 2 Importance of roughness in alluvial channels._____________________ 5 Research program _____________________________________________ 6 Theory of resistance to flow in alluvial channels_______________________ 7 Dependent and independent variables.___________________________ 7 The Pi-theorem.__..________._.___________________________ 10 Summary of theory.___________________________________________ 19 Experimental equipment and procedure._____________________________ 20 The flume.------_-----------_-_-_-___-_-_------------------_- 20 Alluvial bed material____--___-_-______-_-______-___-_____--_-__ 21 General procedure_________-______--_____-_-_-___-_-_-_-_------ 22 Data obtained_______-______-_______-___-_-_-_--_-___-__-_-__- 23 Water-surface slope._______-_______-___-__-___-_____-__-_-_ 23 Discharge _________-___-__-_____-___-_-_________-__-_--___ 24 Water temperature.---------------------.----------------- 24 Depth____-_____-_____--_____._____._____--____.______ 25 Mean velocity___________________________________________ 25 Velocity profiles._____--____-__-_______-_-____-_____----___ 26 Bed material-.__________________________________________ 26 Total sediment load______________________________________ 26 Suspended sediment samples-_______________________________ 27 Bed configuration________________________________________ 27 Presentation of data_______________________________________________ 28 Water-surface slope.___________________________________________ 28 Discharge.___________________________________________________ 28 Depth of flow_____________---____-________--__-_-_-_-_----_--- 32 Kinematic viscosity___.________-__-__--_________-___--__--__-_- 32 Mean velocity_______________________________________________ 32 Velocity profiles._______-____-____---_-____-___-__--____-_-__-_ 33 Bed material..___________________________-_-__-_-_-----_---_-- 34 Total sediment load__________________________________________ 35 Suspended sediment---_--_--_________--_-_--------------_--__- . 35 Bed configuration____________________________________________ 36 m IV CONTENTS Page Observed flow phenomena._________________________________________ A-36 Bed forms in the tranquil-flow regime ____________________________ 39 Plane bed without movement _______________________________ 39 Ripples__-____-_-_________________________________________ 41 Dunes____________________________________________________ 42 Transition from dunes to rapid-flow forms ____________________ 47 Bed forms in the rapid-flow regime_______-_------____________--_ 49 Plane bed with movement._________________________________ 49 Standing waves ___________________________________________ 50 Antidunes ________________________________________________ 52 Analysis of data___________________________________________________ 58 Variation of velocity with depth.________________________________ 59 Variation of total sediment load concentration and Manning n______ 60 Variation of tractive force and total sediment load_________________ 61 Resistance to flow relations _____________________________________ 62 Forms of bed roughness related to size of bed material. ____________ 68 Conclusions._ _____________________________________________________ 73 Literature cited ___________________________________________________ 75 ILLUSTRATIONS Page FIGURE 1. Schematic diagram of the flume___------__---___-____---- A-21 2. Size distribution curve of the bed material..___-_____---___ 22 3. Typical water-surface profiles_-__------_----------------- 29 4. Typical vertical velocity distribution curves at different sta­ tions across the flume.________________________________ 33 5. Major forms of bed roughness___----------------_-------- 37 6. View of bed with no sediment movement (run 14)___________ 39 7. View upstream of ripple configuration (run 9)______________ 41 8. View upstream of dune configuration (run 23)______________ 42 9. Flow over dune configuration similar to that shown in figure 10__________________________________________________ 43 10. View upstream of dune configuration (run 24)______________ 44 11. Three-dimensional flow over the sand bar configuration of figure 12 (run 35)_______________-----_--__---__------- 48 12. View upstream of sand bar configuration (run 35)__________ 49 13. View upstream of a plane bed during rapid flow (run 26)___ 50 14. View downstream of standing wave during rapid flow (run 39) _ 51 15. View upstream of cross-laced configuration (run 27)_________ 51 16. Water surface before the antidune wave starts to build up (run 42)_________________________________________-__ 52 17. View across the flow at an antidune wave that is forming____ 53 18. View upstream of an antidune wave at the point of breaking-- 53 19. Antidune wave after breaking (run 42)____________________ 54 20. View of bed configuration after antidune flow._____________ 54 21. Profiles of the actual water surfaces and bed configurations (runs 44 and 41)______--_-_-_-_-_---_---------------- 56 22. Variation of velocity V with depth D___-------------_--_- 59 23. Variation of shear TO and concentration of total load CT----- 62 24. Variation of V r0/ V*(ATs)d with V#d/». ------------------- 63 CONTENTS V Page FIGURE 25. Variation of (F*d/»0+5 with VrQ/V^(^ys) d and FT. ___._.__ A-64 26. Variation of V*d/v + 5 with [rT0/V*(AY.)d]°-*«/(T r/V?O) I/8 - 66 27. Variation of VdyD*j(VH^D)u* with [OSd/D^/VC^-D/")]2'3 -- 67 28. Criteria for bed roughness in alluvial channels____-_-------- 69 TABLES Page TABLE 1. Summary of data. ________,_-_-__-__________-____-_------ A-30 2. Values for predicting bed form. _-_--__-_--_---_--_---__---- 70 Symbols and Dimensions Dimensions Units A Area of flow cross section.__________-_-__-_.__ L2 ft2 B Width of the flume__.___________--__-_-_-___ L ft C Chezy coefficient of discharge in dimensionless O ^ form which is equivalent to V/V*. CD Drag coefficient for the particle. _ _ _ _ I ~J"_ _______ O CT Concentration of total load.____-____---_-__-_ ppm Cw Concentration of fine material.________________ ppm d Median fall diameter of bed material.__________ L ft d t Median fall diameter of total sediment load___-_ L ft D Average depth of flow________________________ L ft Fr Froude number (Vj-^gD) ______________________ O g Acceleration of gravity.______________________ L/T2 ft/sec2 G Total load being transported-_________________ F/T Ibs/sec h Average height of bed roughness.______-___-_-_ L ft K Any constant,________________-----_-------_ O L Average distance between features of bed rough­ L ft ness. n Manning coefficient of roughness ______________ Li/e fti/e rib Manning coefficient of bed roughness (Einstein). Li/e f t l/6 P Wetted perimeter________________-_---_-.---- L, ft Q Discharge of water-sediment mixture____-__---- L»/T ftS/sec r Relative coefficient of correlation______________ O R Hydraulic radius (A/P) ___________-__--__-_-- L ft Re Reynolds number VD/v _____________-------_- O sfe Shape factor of the channel cross section. ______ O sfp Shape factor of the sediment particle___________ 0 sfr Shape factor for the reach of the stream, sinuosity- O S Slope of energy gradient equal to water surface O slope in steady, uniform flow. t Time____________________________-------_- T sec T Temperature. _ ________________.___--_-_----_ O 0 C V Average velocity based on continuity principal. _ L/T ft /sec Vp Average velocity based on velocity profiles______ L/T ft/sec l7* Shear velocity which is ygDS, VWp- __---_----- L/T ft/sec w Fall velocity of sediment particles. ____________ L/T ft /sec 7 Specific weight of water._____-_________---_-- F/LS lbs/ft3 y, Specific weight of sediment________.____--__-_ F/U lbs/ft3 AY Difference between specific weights of air and F/LS lbs/ft» water. AY, Difference between specific weights of sediment F/L3 lbs/ft3 and water. 5' Thickness of laminar sublayer.________________ L ft v Kinematic viscosity___--_-__----------------- L2/T ft2/sec H Dynamic viscosity.-_____-_________-___------ Ft/L» lb-sec/ft2 CONTENTS VII Dimensions Units P Density of water....-_-_____________-_---_-- Ft2/!4 Slug/ft3 P, Density of sediment... ______________________ Ft2/!4 Slug/ft3 Ap, Difference between density of sediment and Ft2/L4 Slug/ft3 water. o- Relative standard deviation of the size distribu- O tion of the sediment. TO Tractive or shear force developed on the bed, F/L2 lbs/ft2 yDS. re Critical tractive force associated with beginning F/L2 lbs/ft2 of bed movement. GLOSSARY OF TERMS Alluvial channel: A channel whose bed is composed of appreciable quantities of the sediments transported by the flow at a given discharge or greater. Antidunes:
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