Student ID: 10395608 PLYMOUTH UNIVERSITY

Sediment Transport Lab Report HYFM504 COURSEWORK

1

Contents 1.0 Aim and Objectives ......................................................................................................................... 2

2.0 Results............................................................................................................................................. 2

2.1 Observed Bedforms .................................................................................................................... 2

3.0 Calculations ..................................................................................................................................... 4

4.0 Discussion ....................................................................................................................................... 4

5.0 References ...................................................................................................................................... 8

Appendices ........................................................................................................................................... 9

Appendix A – Pictures showing the changes in bedform as the experiment progressed .................. 9

Appendix B – Example Calculations ................................................................................................ 14

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1.0 Aim and Objectives Aim:

To investigate the key processes of sediment transport for unidirectional flow and

non-cohesive materials.

Objectives:

- Perform a laboratory experiment in which the discharge and slope of a flume with

sediment (sand) is change to observe the effects of bedform development.

- Relate the experimental observations and results to those of established theory, and

compare the results with those published in academic texts.

- Investigate/discuss any experimental error produced during the experiment.

2.0 Results Width of channel = 80mm

Table 1: Table showing all data collected during the experiment.

2.1 Observed Bedforms The experiment began with a flat bed; however, within seconds of the pump discharging

water, sediment movement was quickly produced in the form of rolling and a small amount

of saltation. The flat bed from the beginning of the experiment began to change shape. Step

2 produced ripples which were quickly turned into dunes in the flume (Figure 1). The

increase in slope was too fast, translations in the slope increased the mean flow velocity of

the water too much. This produced ripples which formed and disappeared quickly. It was

noticed that sediment was rapidly leaving the flume and depositing in the tank at the end of

the flume. It was also noted that dunes formed at the end of the flume while the middle of

the tank produced ripples and the beginning of the flume produced a flat bed.

Discharge

SettingSlope (%) Sediment Observations

Amplitude

(cm)

Wavelength

(cm)

Average Depth

of Flow (mm)

Step 1 1 0 Rolling/Saltation 0.0 0 11

Step 2 1 0.005 Ripples/bedload/saltation 0.6 14 8

Step 3 1 0.01 Dunes/bedload/saltation 1.0 14 7

Step 4 1 0.01 Dunes/bedload/saltation 1.4 15 12

Step 5 2 0.01 Dunes/saltation/suspended 1.8 10 10

Step 6 3 0.01 Dunes/saltation/suspended 0.8 9 10

Step 7 3 0.01 Dunes/saltation/suspended 1.0 8 12

Step 8 3 0.024 Dunes flattening out 0.4 5 12

Step 9 3 0.027 Suspended (some waves) 0.4 6 10

Step 10 3 0.028 Flat bed/suspended load 0.0 0 7

Step 11 N/A N/A N/A N/A N/A N/A

Measurement of Bedforms

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Steps 3 through 5 produced dunes of increasing amplitude and wavelength; movement of

the sediment began to turn from bedload and saltation into saltation and suspended load.

At the beginning of Step 4, ripples in the dunes appeared (Figure 2). At this point the pump

filter began to clog with sediment. The experiment was then stopped while the inlet pipe

was cleared of sand. The pump was then restarted.

Steps 6 and 7 showed a decrease in the wavelength and amplitude of the formed dunes and

waves. However, the experiment began to struggle pumping water again so it was stopped

and the inlet pipe cleared. It was noticed that the dunes formed were not of similar sizes

along the length, so taking a representative result was difficult. The wavelength and heights

of the dunes and waves also reduced until Step 10 when no obvious waves were produced.

From Step 8 onwards only suspended load was a mechanism of sediment transport.

Although Steps 2 and 3 produced waves of similar amplitude to Steps 7 and 8, a large

reduction in the length of the wavelengths was observed. Another observation of the

experiment suggested that the flume was not producing similar bedforms on both sides of

the tank. When looking at the flume from the side facing the wall, dunes of differing

magnitudes were noted. After Step 10 the pump became blocked by sediment and the

experiment was ended.

Appendix A includes all photos taken during the experiment.

Figure 1: Ripples observed before dunes quickly developed.

Figure 2: Dunes with ripple formation on surface.

Figure 3: Step 7 – dunes and waves of decreasing amplitude.

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3.0 Calculations Calculation of Threshold of Motion of Sediment (Borthwick, 2016):

𝐷∗ = (𝑔 (

𝜌𝑠

𝜌− 1)

𝑣2)

13

∗ 𝐷50 = (9.81 (

26501000 − 1)

(1.36𝑥10−6)2)

13

∗ 0.0003 = 6.1822

𝐷∗ < 200 ∴ 𝜃𝐶𝑅 = 0.30

1 + 1.2𝐷∗+ 0.055(1 − exp(−0.020𝐷∗))

𝜃𝐶𝑅 = 0.30

1 + 1.2 ∗ 6.1822+ 0.055(1 − exp(−0.020 ∗ 6.1822)) = 0.04203

Calculation of τCR (Borthwick, 2016):

𝜏𝐶𝑅 = (𝑔(𝜌𝑠 − 𝜌)𝐷50)𝜃𝐶𝑅 = (9.81 ∗ (2650 − 1000) ∗ 0.0003) ∗ 0.04203 = 0.2041

Table 2: Table showing the calculated mean flow velocity, Reynold’s number, Froude

number, Shield’s Parameter and Particle Reynolds number for each step.

Example calculations of the Mean Flow Velocity, Reynolds Number, Froude Number, Total

Bed Shear Stress, Shields Parameter and Particle Reynolds Number are attached as

Appendix B.

4.0 Discussion From Table 2 it can be seen that most of the steps produced a Reynolds number of above

2000, which according to Hamill (2011, pg. 81) is in the turbulent zone for open channel

flow (Laminar flow < 500; 500 < Transitional flow < 2000; Turbulent flow > 2000). Chadwick,

Morfett and Borthwick (2013) note the conditions of interface between the water and

sediment mean that as turbulent flow is induced in the water, eddy currents form at the

boundary. This generated momentum causes movement of the grains. Therefore, as the

mean flow velocity increases, so does the Reynolds number of the flow and so does the

turbulence. As the turbulence increases, so does the rate, complexity and intensity of the

interaction. According to the turbulence model, turbulent eddies produced will interact with

the sediment creating an uplift force (an upward rate of transport) on the particles

(Borthwick, 2016). As this upward rate of transport increases beyond the fall velocity of the

Mean Flow

Velocity (m/s)

Hydraulic

Radius (m)

Reynold's

Number

Froude

Number

Total Bed Shear

Stress (N/m2)

Shields

Parameter (θ)

Particle Reynolds

Number

Step 1 0.284 0.0086 1802 0.865 0.00 0.000 0.000

Step 2 0.391 0.0067 1915 1.394 0.33 0.067 3.989

Step 3 0.446 0.0060 1956 1.704 0.58 0.120 5.333

Step 4 0.260 0.0092 1768 0.759 0.91 0.186 6.638

Step 5 0.513 0.0080 3015 1.636 0.78 0.162 6.180

Step 6 0.775 0.0080 4559 2.474 0.78 0.162 6.180

Step 7 0.646 0.0092 4383 1.882 0.91 0.186 6.638

Step 8 0.646 0.0092 4383 1.882 2.17 0.448 10.284

Step 9 0.775 0.0080 4559 2.474 2.12 0.436 10.154

Step 10 1.107 0.0060 4850 4.225 1.64 0.337 8.923

Step 11 N/A N/A N/A N/A N/A N/A N/A

(3)

(2)

(1)

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particles then the particles will reach equilibrium and become suspended. This was

observed during the experiment and can be seen to correlate with the theory in Table 3

(Reynolds numbers exceeding 2000 correlate with observed suspended transport –

highlighted in green). Therefore this turbulence induced the formation of ripples and dunes.

Table 3: Table showing the relationship between the Reynolds number and the suspended

load & Froude number and observed transport mechanism.

Steps 1 to 4 of the experiment also note Reynolds numbers in the transitional flow regime.

As Hamill (2013) notes, Reynolds’ experiments to determine the Reynolds equation and

classify flow regimes into laminar, transitional and turbulent flow relied upon a subjective

judgement of when the flow became turbulent. It is stated that in the transitional range that

other factors such as roughness were important. This may account for small amounts of

suspended load in Steps 3 & 4 (deemed insufficient for comment above). However, this

statement is based on regime flow in pipes and not open channel flow. As in steps 1 to 4,

the flow of water is interacting with the sediment but the intensity and turbulence of the

water was not enough to cause much suspended sediment transport.

Chanson (2004, cited in Borthwick, 2016) suggests a relationship between the mean flow

velocity and the bed shear stress. It is noted that in subcritical flow, ripples and dunes will

occur. At the transition between subcritical and supercritical a flatbed will occur. Further

increasing the Froude number produces standing waves and antidunes. As Table 3 above

shows, the theory relating Froude number to observed bedforms does not correlate well.

Only Step 4’s observations correlate with this theory. The diagram provided by Chanson

(2004, cited in Borthwick, 2016) does not provide specific ranges of Froude numbers for the

observed bedforms. According to Bennett (1997), if the particle size is below 0.6mm and the

experiment begins with a flattened bed then ripples and dunes will occur with a low Froude

number below 1. Flat bed should be observed at a Froude number between 0.8 & 0.95.

Antidunes and chutes & pools should occur between 1 and 1.5.

Although the order of observations does match the theory of Chanson (2004, cited in

Borthwick, 2016) and Bennett (1997), it can be seen from Table 3 that the Froude numbers

do not match with the established theory. Indeed, it is noted by Graf (1971, pp. 278) that

the Froude number measured in the laboratory may be different to that observed in a river.

Chanson’s (2004, cited in Borthwick, 2016) graph comparing Froude numbers to bedform is

based on beaches (not unidirectional flow - as in the experiment). It is theorised that this

perceived difference may also be due to inaccurate and imprecise measurements of the

Reynold's

NumberFroude Number Sediment Observations

Step 1 1802 0.865 Rolling/Saltation

Step 2 1915 1.394 Ripples/bedload/saltation

Step 3 1956 1.704 Dunes/bedload/saltation

Step 4 1768 0.759 Dunes/bedload/saltation

Step 5 3015 1.636 Dunes/saltation/suspended

Step 6 4559 2.474 Dunes/saltation/suspended

Step 7 4383 1.882 Dunes/saltation/suspended

Step 8 4383 1.882 Dunes flattening out/suspended

Step 9 4559 2.474 Suspended load (some waves)

Step 10 4850 4.225 Flat bed/suspended load

Step 11 N/A N/A N/A

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depth of flow of the water. Evidence of this can be seen in Table 1 in which Steps 7, 8 and 9

although increasing in slope (which would result in a faster mean flow velocity and

therefore shallower depth of flow) does not at first decrease in depth. The error could also

be due to the pump discharging varying amounts of water. It is the view of this report that

human error is more likely to be at fault, as although several measurements were made

along the flume at each stage, accurate measurements were difficult to achieve due to the

highly irregular bed depth.

Representative bedforms at each stage were measured for their observed amplitude and

wavelength. It can be seen below in Table 4 that the peak amplitude and wavelengths occur

at Steps 5 and 4 respectively as this is where the dunes were observed at their peak

dimensions. By using the equations listed in Borthwick (2016) it can be seen that the

observed amplitude is not dissimilar to the calculated amplitude (Step 2 highlighted in green

was calculated using the ripple formulae). However, the peak amplitudes calculated

continue to rise until step 7 which is beyond that of the observed results. Calculated

wavelength against observed wavelength differ considerably in the initial steps however

convergence of the values seems to occur beyond Step 5. Robert (2003, pp. 94) states that

ripple height should be somewhere between 1 and 3 cm and a wavelength usually smaller

than 40cm. The book also noted that dunes may vary from a few centimetres to several

metres in height. Borthwick (2016) presents typical ripple wavelength values of 0.14m and

wave heights of 0.016m. The values stated by Borthwick (2016) match with those found in

the experiment more readily.

Table 4: Comparison of height and wavelength of ripples and dunes to collected data.

The variability in the calculated wavelengths and wave heights may again be due to

inaccuracies in the depth of flow measurement (relating to the hydraulic radius as a

parameter in τ0S) and a slope % that may not accurately reflect the slope of the flume (a

parameter of τ0S). It was noted at the beginning of the experiment that the flume must be

set to a negative slope angle to register as a flat surface when compared with a spirit level.

Therefore, an informed judgement was made as to the true reading of the slope angle. As

mentioned in Section 2.1, the observed bedforms were of different sizes on both sides of

the flume. Unfortunately, due to time constraints and a lack of space, the observed sizes of

dunes on the opposite side of the flume could not be measured. It is theorised that this may

have occurred because the base of the flume is not flat and instead leans towards the wall

slightly. Therefore, should the experiment be repeated, it must be calibrated to obtain more

Observed

Amplitude (m)

Observed

Wavelength (m)

Calculated

Amplitude (m)

Calculated

Wavelength (m)

Step 1 0.000 0.000 0.000 0.000

Step 2 0.006 0.140 0.043 0.300

Step 3 0.010 0.140 0.004 0.051

Step 4 0.014 0.150 0.008 0.088

Step 5 0.018 0.100 0.006 0.073

Step 6 0.008 0.090 0.006 0.073

Step 7 0.010 0.080 0.008 0.088

Step 8 0.004 0.050 0.007 0.088

Step 9 0.004 0.060 0.006 0.073

Step 10 0.000 0.000 0.005 0.051

Step 11 N/A N/A N/A N/A

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accurate and representative results. Error of the measurements taken may also exist due to

the varying size and nature of the bedforms observed; taking a representative reading was

therefore difficult to achieve.

As can be seen in Table 1, all steps conducted in the experiment exceed the critical Shields

parameter of 0.04203 (Equation 2). The greatest Shields Parameter value is 0.448, therefore

the sediment transport is either ripples or dunes according to Borthwick (2016, pp. 14), as

all values are below 0.8. Table 2 also shows that the threshold of motion is also immediately

exceeded at Step 2. When the Shields parameters and associated particle Reynolds

Numbers are compared with the range of values presented in Figure 4 below, all values lie

within the observations made during the experiment correlate with this information i.e. the

answers lie within the ripples and dunes section of the graph. It is difficult to be more exact

with whether ripples or dunes should occur as there is no line for sediment particles of

0.3mm.

It should be noted that sediment motion

was seen throughout the experiment at all

Steps. All flow conditions excluding Steps

1 and 11 had a total bed shear stress value

(τCR) greater than 0.2041. The

experimental observations showing

sediment movement at all stages relates

to this finding. Calculations for Step 1

show that there is no shear stress acting on

the bed when sediment motion occurs. This is

because the equation used to evaluate the

total bed shear stress is reliant upon a bed

slope. Therefore, no value could be obtained.

Antidunes were not observed during the experiment. This phenomenon may have occurred

during Step 11, however as noted above in Section 2.1, the amount of sediment leaving the

pump caused an insufficient amount of water to circulate for Step 11. Although this

experiment was related specifically to unidirectional flow in which antidunes may form,

when comparing this to the real world this phenomenon is very rare due to the large

average flow velocity to flow depth (Robert, 2003, pp. 94).

A further source of experimental error (alluded to in Section 2.1) is from ‘bedform

hysteresis’, whereby the discharge in the flume changes but the bedforms do not have

enough time to adapt to the new flow regime (Armfield ,2015). This may have had a large

effect on the results as the experiment was conducted quickly to try and avoid pump

blockages. Indeed, it was observed during the experiment that different bedforms occurred

at different positions along the flume (example in Appendix B – Step 7 photos). However, as

discussed above, it is the conclusion of this report that the depth of flow is inaccurate,

thereby causing errors in the calculations. Doing repeats is recommended due to the large

amount of errors that have occurred.

Figure 4: Graph of Shields parameter vs.

particle Reynolds number (Marriott, 2009,

cited in Borthwick, 2016)

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5.0 References Armfield (2015) Sediment Transport Demonstration Channel – S8MkII. [Data sheet available at:

http://discoverarmfield.com/en/products/view/s8/sediment-transport-demonstration-channel

(Accessed: 19 April 2016).

Bennett, J. (1997) Resistance, Sediment Transport, and Bedform Geometry Relationships in Sand-Bed

Channels. Available at: http://water.usgs.gov/osw/techniques/workshop/bennett.html (Accessed:

17 April 2016).

Borthwick, M. (2016) ‘Sediment Transport in Rivers and Estuaries’. Advanced Hydraulic Engineering

[Online]. Available at: dle.plymouth.ac.uk (Accessed: 14 April 2016).

Chadwick, A., Morfett, J. and Borthwick, M. (2013) Hydraulics in Civil and Environmental Engineering.

5th edn. UK: Taylor & Francis Group.

Graf, W. (1971) Hydraulics of Sediment Transport. 1st edn. United States of America: McGraw-Hill,

Inc.

Hamill, L. (2011) Understanding Hydraulics. 3rd edn. Basingstoke: Palgrave MacMillan.

Robert, A. (2003) River Processes: An Introduction to Fluvial Dynamics. England: MPG Books Ltd.

University of Delaware (no date) Open Channel Flow. Available at:

udel.edu/~inamdar/EGTE215/Open_channel.pdf (Accessed: 15 April 2016).

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Appendices

Appendix A – Pictures showing the changes in bedform as the experiment progressed Step 3:

10

Step 4:

11

Step 6:

12

Step 7:

13

Step 8:

14

Appendix B – Example Calculations Example calculation for the mean flow velocity (Step 2):

𝑉 = 𝑄

𝐴=

0.00025

6.4𝑥10−4 = 0.391𝑚/𝑠

Example calculation for Reynold’s number (Step 2): (University of Delaware, no date)

𝑅𝑒 = 𝑉𝑅

𝑣=

0.391 ∗ 6.667𝑥10−3

1.36𝑥10−6 = 1915

Example calculation for the Froude number (Step 2): (Hamill, 2011)

𝐹 = 𝑉

√𝑔𝐷𝑀

= 0.391

√9.81 ∗ 0.008= 1.394

Example calculation for the Shield’s Parameter (Step 2): (Borthwick, 2016)

Total bed shear stress, τ0 = ρgRS0 = 1000*9.81*6.667x10-3*0.005 = 0.33

𝜃 = 𝜏0

(𝑔(𝜌𝑠 − 𝜌)𝐷)=

0.33

(9.81 ∗ (2650 − 1000) ∗ 0.0003)= 0.067

Example calculation for the Particle Reynolds number (Step 2): (Borthwick, 2016)

Shear velocity, u* = √(τ0/ρ) = √(0.33/1000) = 0.0182

𝑅𝑒∗ = 𝑢∗𝐷50

ν=

0.0182 ∗ 0.0003

1.36𝑥10−6= 3.989

Example calculation of Dune height (Step 3): (Borthwick, 2016)

Ts = (0.58 – 0.2041)/0.2041 = 1.863427

∆𝑠 = 0.11ℎ (𝐷50

ℎ)

0.3

(1 − 𝑒−0.5𝑇𝑠)(25 − 𝑇𝑠)

∆𝑠 = 0.11 ∗ 0.007 ∗ (0.0003

0.007)

0.3

∗ (1 − 𝑒−0.5∗1.863)(25 − 1.863) = 0.00419