the effect of bed roughness on velocity profile

Rivers’04

1st International Conference on Managing Rivers in the 21st Century: Issues & Challenges

The Effect of Bed Roughness on Velocity Profile in Open Channels

A. MAHDAVI, PHD student, Department of Irrigation and Reclamation Engineering, University of Tehran, Tehran, Iran

M.H. OMID, Assistant Professor, Department of Irrigation and Reclamation Engineering, University of Tehran, Tehran, Iran ABSTRACT The effect of bed roughness and bed load movement on flow velocity profile in an open channel with uniform flat-bed is experimentally investigated. Experiments were performed in a tilting channel of glass sides and smooth bed made of Perspex, and of rectangular cross-section 250 mm wide and 12.5 m long. Two different grain sizes with diameter of 0.5 and 2.84mm were used for the roughening of the bed and sediment injection. Sediment injection was performed with the same size of particles used for roughening the bed. Point velocities were measured by a 10 mm propeller current meter. The results indicate that the logarithmic law for velocity profile is valid for different bed conditions and bed load concentrations. However, lower part of the profile is influenced by the bed roughness resulting steeper slope of the profile in logarithmic region. Since the slope of this profile increases, shear stress and consequently friction factor increases, affecting the bulk of flow to reduce the mean flow velocity. Keywords: Bed roughness, Velocity profile, Bed load, Shear stress. 1 Introduction The velocity profile is closely related to the friction factor and boundary roughness, though the connection had received relatively little attention until 1980. Because the friction factor can be estimated from the bulk measurements without having to obtain the velocity profile, earlier works until 1980 had tended to consider the two separately, in many cases ignoring the velocity profile altogether since the friction factor is often of more direct engineering interest. The renewal of interest in the characterization of velocity profiles due to work of Itakura and Kishi (1980) and particularly Coleman (1981, 1986) had led to further debate concerning the friction factor.

In open-channel flow the velocity is not uniformly distributed. In this research, only vertical velocity profile is studied. In case of gravel bed and turbulent flow the vertical velocity profile is often assumed to be logarithmically distributed (e.g.

Chow, 1959; French, 1986; Graf 1998 and Ferro, 1999). Logarithmic velocity profile can be shown by: (1)

where u= velocity [m/s] in distance y[m] from the bed; u*= the shear velocity [m/s]; κ = Von Karman constant; and y0= the integral constant. The flow can be hydraulically either smooth or rough. Hydraulically smooth flow occurs when the surface irregularities are so small that all roughness elements are entirely submerged in the laminar sub layer (Chow, 1959). Therefore, the bed roughness will not affect the velocity distribution. According to Graf (1998) and Schlichting & Gersten (2000) the flow is smooth if:

(2) Where ν = kinematic viscosity [m2/s]; and k is the roughness height [mm].

⎟⎟⎞⎛

=ylnuu

⎠⎜⎜⎝

∗

0yκ

50 * <<ν

sku

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Substituting y0 for smooth channel in equation 1, one gets: (3) The flow is rough when bed roughness is so large that it produces eddies close to the bottom (Liu, 2001). There is no viscose sub layer and the velocity distribution is affected only by bed roughness. According to Graf (1998) and Schlichting & Gersten (2000) the flow is hydraulically rough if: (4) Substituting y0 for rough channel in equation 1, it follows: (5) In this equation the roughness element ks, may be considered as the sum of the skin roughness, and sediment transport roughness (suspended load and the bed load transport).

In studies of flow with suspended sediment, two concerns often raised are the effects of suspension on both velocity distribution and flow resistance. Based on the experimental results of Vanoni (1946), Einstein and Chein (1955) and Elata and Ippen (1961), as the sediment concentration increases, the Von Karman constant becomes progressively smaller than that of the clear water value of 0.4. However, this view is not universally endorsed. Imamoto, et al. (1977) found that κ increases with sediment concentration in their experiments while Fukuoka (1980) and Itakura and Kishi (1980) suggested that the value of κ does not change.

Coleman (1981) analyzed his own data and reexamined the data from earlier experiments to show that the change in κ, which was found in the earlier works, were due to incorrect application of logarithmic velocity distribution to the outer flow

region where the logarithmic law is really not valid. By applying the logarithmic law only to the region close to the bottom boundary, Coleman found that the presence of suspended sediment has no effect on the value of κ. The value of κ was found to conform to the law of the wake which was introduced by Coles (1956) for boundary layer flows. It appears that Coleman (1981) has presented the most convincing argument to date on the effects of suspended sediments on the velocity distribution in open channels. The general velocity profile given by the logarithmic law plus a wake function seems to be valid for all of the flow depth outside of viscose sub layer.

5.5log75.5 +

In compare to suspended load transport, a few studies were found in the literature regarding the effects of bed load movement on flow resistance and velocity distribution. The generally accepted view is that bed load extracts momentum from the flow which causes a reduction of flow velocity and increase of apparent roughness length (Ryckoczi 1967, Kennedy 1969, Wang & Chien 1985, Mclean 1992, Song et al. 1998, Begeron et al. 1999). But some researchers believe that bed load movement has no effect on flow resistance (Einstein & Barbarosa 1952, Vanoni & Nomicos 1960, Yang & Hirano 1995).

In this research, the effects of skin roughness and bed load movement with different concentrations on flow resistance and velocity profile are experimentally investigated. 2 Experimental SET UP and

procedure Experiments were performed in a tilting channel of glass sides and smooth bed made of Perspex, and of rectangular cross-section 250 mm wide and 14 m long. The downstream end of the channel is provided with a sediment trap with a collecting basket and the weight of sediments

⎟⎠⎝ νu⎞

⎜⎛= ∗

∗

yuu

70>u*

νsk

5.8log5 +⎟⎞⎛

=yu 75. ⎟

⎠⎜⎜⎝∗ Sku

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collected in the basket is continuously measured by a digital weighing scale. Downstream of the sediment trap is a tailgate consisting of a set of horizontal rotating flaps to provide various degrees of opening for the water to flow through. The tailgate is used to adjust the depth of water in the channel without causing undue backwater effects into the channel. In each of the experiments clear water is supplied at a steady rate from an overhead constant head tank. For experiments with the rough bed, a single layer of uniform sand was glued onto the Perspex bed. The same size of sand was injected to the flow using a screw feeder system to produce bed load at the beginning of the flume. Two different grain sizes d=0.5mm and d=2.84mm were used in the experiments. Point flow velocities were measured by a 10 mm propeller current meter.

The experiments were carried out with (i) clear water over smooth and rough beds, and (ii) sediment laden flows over smooth and rough beds. In the first series, a number of preliminary experiments were carried out to determine the friction factor f, for smooth and rough rigid beds. Various slopes of the channel and velocities of flow were considered in these experiments. This information was then used to set the depth of flow before injecting sediment at the upstream end in the main experiments.

Prior to the experiments with sediment-laden flow, for a given slope of the channel and discharge of water, a uniform flow without sediments was first obtained by adjusting the tailgate to attain a prescribed depth. Different concentrations of sediments were then injected into the flow at constant rate at the upstream end of the flume. The rate of sediment supply was kept constant by adjusting the feeder and keeping the sand level coinciding with the top level of the container. Flow measurements were made for various injection rates less than the rate at which initiation of sediment deposition on the bed was observed. Bed load

particles were collected in the sediment trap provided at the downstream end of the flume to be removed periodically. For each injection rate I expressed in terms of mass rate, the corresponding volumetric concentration of sediment C is simply

s

ICQS

= (6)

Where Q = the water discharge and Ss = the sediment density, is taken to be 2650 kg/m3. The experimental conditions are summarized as follows: sediment diameters used: 0.5 and 2.84 mm sediment concentration: 0.0025-0.0075 water depth: 25 mm to 250 mm mean velocity: 0.35 to 1.2 m/s bed slopes used: 1:1000, 2.5:1000, 3:1000 For each sediment concentration, two or three flow velocity profiles were measured along the vertical centerline of the cross-section of flow at a position located 8.0 m downstream from the location where sand particles were injected into the flow. Starting from 10mm above the bed, which was dictated by the size of the current meter, velocities were measured at vertical intervals of 5mm up to 20% of water depth and then at 10mm intervals up to the water surface. The measured velocity profiles were then averaged to obtain the mean velocity profile corresponding to a particular sediment concentration. The mean bulk velocity U of each averaged profile was then obtained by integrating the profile over the whole flow depth. The shear velocity u* and the friction factor f were then calculated from the averaged velocity profile using the equations for velocity profile in rough turbulent flow and shear velocity.

3 Results Figure 1 shows the velocity profiles in normal and semi-log scales for clear water condition. These profiles are presented to show how the experimental results fit the logarithmic law given by equation 2.

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0

4

8

12

16

50 60 70 80 90 100u (cm/s)

y (c

m)

y = 0.0799x + 0.6739u*/k=S=0.0799u*=0.0799*0.4=0.0032 m/s

20

30

40

50

60

70

80

90

100

-1 0 1 2 3Ln (y)

u (c

m/s

)

Figure 1 Velocity profile related to clear water on smooth bed. 3.1 Effects of bed roughness on velocity

distribution Two sets of velocity distributions related to the same discharge and bed slope are shown in figure 2a and 2b to show how bed roughness changes the velocity distributions. Figure 2a shows velocity distributions for discharge of 30 lit/s on smooth and rough bed. It can be seen that with the same slope, as the bed roughness increases, the

velocity decreases especially in lower part of the velocity profile. In other word, the amount of decrease in the lower part of the profile is more than the upper part. The velocities related to the bed roughness of 2.84mm are higher because the slope of these experiments is more than the others. The amount of this increase in the upper part is more than the lower part. We can also see these results in figure 2b that is due to discharge of 40 lit/s.

Q=30S=0.002 ,h=16 cmS2.84=0.005 ,h=13.5 cmClear Water

0

4

8

12

16

20

40 50 60 70 80 90 100 110u(cm/s)

y(cm

) Rough Bed,d=2.84Smooth BedRough Bed,d=0.5

Q=40S=0.002 ,h=20 cmS2.84=0.004 ,h=18 cmClear Water

0

4

8

12

16

20

40 50 60 70 80 90 100 110u(cm/s)

y(cm

) Rough Bed,d=2.84Smooth BedRough Bed, d=0.5

Figure 2 Velocity profiles on smooth and rough bed with different roughness.

Q=30S2.84=0.005 ,h=13.5 cmS=0.002 ,h=16 cmClear Water

a=17.09

a=7.51

a=10.40

40

50

60

70

80

90

-0.5 0 0.5 1 1.5ln(y)

u(cm

/s)

Rough Bed,d=2.84Smooth BedRough Bed,d=0.5

Q=40S=0.002 ,h=20 cmS2.84=0.004 ,h=18 cmClear Water

a=8.32

a=16.75

a=10.77

40

50

60

70

80

90

-0.5 0 0.5 1 1.5ln(y)

u(cm

/s)

Smooth BedRough Bed,d=2.84Rough Bed,d-0.5

Figure 3 Velocity distribution with semi-log scales for logarithmic part of profiles in figure 2.

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As it can be seen from the figures, changes in discharge and bed slope affect the upper part of flow region while when the bed roughness is changed, the lower part is more affected. This makes the logarithmic part of velocity distribution steeper resulting higher shear velocity. So we expect more friction factor in rough beds. This is shown in figure 3. This figure shows the logarithmic part of velocity profiles presented in figure 2 in a semi-logarithmic scale (a is line slope).

As shown in figure 3, when the bed roughness increases, a and u* are increased. This increase together with a reduction in mean velocity will increase the friction factor f, according to equation 7.

2*8 ⎟

⎠⎞

⎜⎝⎛=

Uuf (7)

in which U= mean flow velocity.

3.2 Effects of bed load roughness in velocity profile

Figure 4a and 4b show the effect of size and concentration of injected sediments on flow velocity distributions.

Figure 4a shows the velocity distributions related to smooth bed (clear water and rough bed with diameter of 0.5 and 2.84mm). It shows that the increase of diameter and concentration causes a reduction in flow velocity.

Figure 4b shows the velocity distribution related to smooth bed (clear water and sediment injection (d=0.5mm) with two sediment concentration. It is clear that sediment injection causes a reduction in velocity especially in lower part of velocity profile. It also shows that increasing sediment concentration causes more reduction of velocity in lower part of velocity distribution profile.

The logarithmic parts of the velocity profiles of Figure 4 are plotted in semi-logarithmic scales in Figure 5 to show the effect of sediment injection on the lower part of the velocity profile. It shows that sediment injection caused an increase in slope of logarithmic part of velocity distribution and shear velocity. Further, this shows increase of concentration also causes more increase in shear velocity.

Figure 4 Effect of sediment injection with different diameter and concentration on flow velocity in smooth bed.

Q=40S=0.002h=20.5 cmSmooth Bed

0

4

8

12

16

20

50 60 70 80 90 100u(cm/s)

y(cm

) Clear Waterd=0.5, c=0.008d=2.84, c=0.0126

Q=40S=0.002h=20.5 cmSmooth Bedd=0.5 mm

0

4

8

12

16

20

50 60 70 80 90 100u(cm/s)

y(cm

)

Clear Waterc=0.0026c=0.008

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Q=40S=0.002h=20.5 cmSmooth Bed a=8.32

a=12.03 a=12.80

40

50

60

70

80

90

-0.5 0 0.5 1 1.5 2ln(y)

u(cm

/s)

Clear Waterd=0.5,C=0.008d=2.84,C=0.0126

Q=40S=0.002 ,d=0.5mmh=20.5 cmSmooth Bed a=8.32

a=11.26

a=12.88

40

50

60

70

80

90

-0.5 0 0.5 1 1.5ln(y)

u(cm

/s)


Figure 5 Mean velocity against ln (y) for logarithmic part of velocity profiles in figure 4.

Figures 6 show the effect of different concentrations on velocity distribution related to rough bed. Figure 6a shows velocity distributions related to rough beds with d=0.5mm (clear water and two different concentrations of sediment injection with d=0.5mm). It can be seen that, firstly, sediment injection causes a reduction in velocity, especially in lower part of profile. Secondly, increase of

concentration has increased this effect. This is also shown in Figure 4b which is due to sediment size d=2.84mm.

The velocity profile of Figure 6 is also plotted in a semi-logarithmic scale in Figure 7 to see the effect of sediment injection with different concentrations on shear velocity. It can be seen that the sediment injection increase the shear velocity.

Q=40.2S=0.002h=20 cmRough Bedd=0.5

0

4

8

12

16

20

50 60 70 80 90 100 110 120u(cm/s)

y(cm

)

Clear waterC=0.0026C=0.0037

Q=45.13S=0.005h=17.5 cmRough Bedd=2.84

0

4

8

12

16

20

50 60 70 80 90 100 110 120u(cm/s)

y(cm

)

Clear WaterC=0.0026C=0.0095

Figure 6 Effect of sediment injection with different concentration on flow velocity in smooth bed.

Q=40.2S=0.002h=20 cmRough Bedd=0.5

a=10.77

a=12.45

a=12.93

50

60

70

80

-0.5 0 0.5 1 1.5ln(y)

u(cm

/s)


Q=45.13S=0.005h=17.5 cmRough Bedd=2.84

a=13.26

a=18.66

a=21

.68

50

60

70

80

90

100

-0.5 0 0.5 1 1.5 2ln(y)

u(cm

/s)

Clear Water

c=0.0026c=0.0095

Figure 7 Mean velocity against ln (y) for logarithmic part of velocity profiles in figure 6.

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4 Conclusion The effect of bed roughness and bed load movement on flow velocity profile in an open channel is experimentally investigated. Following are the conclusions: • Experimental results of smooth and

rough bed fit the logarithmic law of flow velocity distribution profile,

• changes in discharge and bed slope influence the upper part of velocity profile,

• increase in roughness elements (skin roughness and bed load roughness) affect the lower part of profile making the logarithmic part of velocity profile steeper. Since the slope of this profile increases, shear stress and consequently friction factor increases, affecting the bulk of flow to reduce the mean flow velocity

References 1. Bergeron, N. E. & Carbnneau, P. 1999.

The Effect of Sediment Concentration on Bed Load roughness. J. Hydrological Processes 13(16): 2583-25892.

2. Colman, N. L. 1981. Veloeity profiles with suspended sediment. J. Hydr.Res 19(3): 211-229

3. Colman, N. L. 1986. Effects of suspended sediment on the open channel velocity distribution. Water Resources Research 22(10): 1377-1384.

4. Itakura, T. & Kishi, T. 1980. Open channel flow with suspeneded sudiments. Journal of Hydraulic Engineering, ASCE 106(8): 1325-1343

5. Khullar, N. K., Kothyari, U. C. & Ranga Raju, K. G., 2002. The effect of suspended sediment on flow resistance. 5th International conference on hydro-science and engineering, September, 18-21, Warsaw, Poland.

6. Lau, Y. L. 1983. Suspended sediment effect on flow resistance. J. Hydr. Eng., ASCE 109(5): 757-763.

7. Lyn, D. A. 1991. Resistance in Flat-Bed Sediment-Laden Flows. J. Hydraulic Engineering 117(1): 94-114.

8. Mclean, S. R. 1992. On the calculation of suspended load for non cohesive sediments. J. Geophys. Res. 97(C4): 5759-5770.

9. Pullaiah, V. 1978. Transport of fine suspended sediment in smooth ved channels. ph.D thesis,University of Roorkee, Roorkee.

10. Ryckoczi, L. 1967. Experiment study of flume bed roughness. Symp. Pf 2nd Int. Assn. for Hydr. Res. Vol. 1, Fort Collins, Colo.: 181-186.

11. Song, T., Chiew, Y. M. and Chin, C.O. 1998. Effect of Bed Load Movement on Friction Factor. J. Hydraulic Engineering 124(2): 165-167.

12. Vanoni, V. A. & Nomicos, G. N. 1960. Resistance properties of sediment-laden streams. Trans. Am. Soc. Civ. Engrs., ASCE, 125: 1140-1175.

13. Vanoni. V.A & Nomecos, G.N. 1960. Resistance properties of sediment laden streams Transactions of ASCE. pp. 1140-1175.

14. Yang, Y. & Hirano, M. 1995. A discussion on uniform flow in open channel with moveable gravel bed. J. Hydraulic Research 33(6): 877-879.

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