MIT 12 090 - THE SEDIMENT TRANSPORT RATE (12 pages)

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THE SEDIMENT TRANSPORT RATE



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THE SEDIMENT TRANSPORT RATE

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Pages:
12
School:
Massachusetts Institute of Technology
Course:
12 090 - Introduction to Fluid Motions, Sediment Transport, and Current-Generated Sedimentary Structures
Introduction to Fluid Motions, Sediment Transport, and Current-Generated Sedimentary Structures Documents
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CHAPTER 13 THE SEDIMENT TRANSPORT RATE INTRODUCTION 1 By the sediment transport rate also called the sediment discharge I mean the mass of sedimentary material both particulate and dissolved that passes across a given flow transverse cross section of a given flow in unit time Sometimes the sediment transport rate is expressed in terms of weight or in terms of volume rather than in terms of mass The flow might be a unidirectional flow in a river or a tidal current but it might also be the net unidirectional component of a combined flow even one that is oscillation dominated Only in a purely oscillatory flow in which the back and forth phases of the flow are exactly symmetrical is there no net transport of sediment Here we focus on the particulate sediment load of the flow leaving aside the dissolved load which is important in its own right but outside the scope of these physics based notes 2 Over the past hundred plus years much effort has been devoted to accounting for or predicting the sediment transport rate Numerous procedures usually involving one or more equations or formulas have been proposed for prediction of the sediment transport rate These are commonly called sedimentdischarge formulas The term formula here is in some cases a bit misleading some of the procedures involve the use of reference graphs in addition to mathematical equations No single formula or procedure has gained universal acceptance and only a few have been in wide use None of them does anywhere near a perfect job in predicting the sediment transport rate which is understandable given the complexity of turbulent two phase sedimenttransporting flow and the wider range of joint size shape frequency distributions that are common in natural sediments Prediction of the sediment transport rate is one of the most frustrating endeavors in the entire field of sediment dynamics 3 In this brief chapter we focus on the concept of the sediment transport rate more than on the procedures by which it might be predicted it would take a lot of additional space in these course notes to do justice to the details of even the small number of sediment discharge formulas that are in common use THE SEDIMENT LOAD AND THE SEDIMENT TRANSPORT RATE The Sediment Load 4 First you must be clear on the distinction between the sediment load and the sediment transport rate Recall from Chapter 10 that the load is all of the sediment that is being moved by the flow at a given time Figure 13 1 shows how 445 to conceptualize the sediment load In Figure 13 1 you can imagine somehow freezing a block of the flow that contains both water and particulate sediment and then melting the block to collect the sediment in the block That sediment is the load You can think of the sediment load as the depth integrated sediment mass above a unit area of the sediment bed d L sediment load c y dy 0 where c is the local time average sediment concentration Then the average concentration of transported sediment C is equal to L d Figure 13 1 Conceptualizing the sediment load 5 Just as a review of what was said about the sediment load back in Chapter 10 here are some points or comments about the sediment load There is no fundamental break between the bed load and the suspended load For a given particle that is susceptible to suspension in a given flow the particle at various times might be traveling as either bed load or as suspended load or it might temporarily be at rest on the bed surface or within the active layer 446 The ranges of particle size for the bed load and the suspended load in a given flow overlap The suspended bed material load is not really suspended it is merely traveling temporarily in the turbulent flow above the bed The bed load layer is thin relative to the suspended load layer The bed load layer is the lower boundary condition of the suspended load layer The sediment concentration in the bed load layer is ordinarily much greater than that in the suspended load layer The Sediment Transport Rate 6 The sediment transport rate is commonly denoted by Qs What is more useful however and what you are likely to encounter if you have to deal with sediment transport is the sediment transport rate per unit width of the flow That is called the unit sediment transport rate it is often denoted by qs Think in terms of a vertical slice of the flow with unit width and oriented parallel to the flow Which you use depends upon whether you are interested in how much sediment the entire flow carries Qs or in the inherent intensity of the sediment transport qs 7 Below are descriptions of three ways of conceptualizing the sediment transport rate Each represents in principle although not necessarily in practice a way of measuring the sediment transport rate The magic screen Obtain a magic screen which when installed across the flow allows you to measure the mass mi of each of the n particles that pass across the screen in unit time Figure 13 2 Then n qs mi widthof flow 1 The magic vacuum suction trap Install a slot across the entire width of the flow that allows you to remove all of the particles both bed load and suspended load that pass across the cross section of the flow above the slot Figure 13 3 Think in terms of a magic vacuum cleaner that sucks all of the sediment particles out of the flow and into the trap In real life that would not be extraordinarily difficult for the bed load but virtually impossible for the suspended load Suppose that you thereby extract a mass M of sediment that would have been transported across the location of the cross section in an interval of time T Then 447 the unit sediment transport rate qs would be equal to M T divided by the width of the flow Figure 13 2 Conceptualizing the measurement of the sediment transport rate by use of a magic screen Depth integrated sampling Figure 13 4 Along a vertical in the flow measure the downstream component of velocity vi of all of the particles in a tiny imaginary cube in the flow with volume V at a given instant Then multiply vi by the mass mi of the particle and sum over all n particles found Divide the result by V to obtain the transport rate per unit area and integrate the result over flow depth on a vertical traverse That give you qs for that cross stream position in the flow 8 It is notoriously difficult to measure the sediment transport rate even in controlled settings in laboratory flumes In a flume if only bed load is being transported you can arrange a sediment trap in the form of a


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