Determination of Flow Resistance Coefficients Due to Shrubs and Woody Vegetation

Transcription

1 ERDC/CL CETN-VIII-3 December 000 Determination of Flow Reitance Coefficient Due to hrub and Woody Vegetation by Ronald R. Copeland PURPOE: The purpoe of thi Technical Note i to tranmit reult of an experimental invetigation into the effect of vegetation (particularly ground cover plant, mall tree, and hrub) on flow reitance. INTRODUCTION: An important conideration for determining the tage-dicharge relationhip in river and tream i the effect or influence of vegetation on the overall head lo along a channel and in the overbank. Plant in the floodplain and along the bank can increae or even decreae the effective flow reitance. The vegetation may be natural or it may have been planted to improve aethetic or habitat, to prevent eroion, or for other reaon. ydraulic loe and drag due to actual plant were meaured at the Utah tate Univerity Water Reearch Laboratory utilizing a large wide flume and a maller ectional flume. Reearch in the flume reulted in the collection of data from more than 0 experiment with 0 different plant pecie. Experiment were conducted with both homogeneou and mixed plant grouping. ingle-tem and multiple-tem plant were included in the plant type evaluated. Plant with and without leave were evaluated. Plant denity, pacing, and ize were varied in the experiment. Plant were evaluated over a range of velocitie and depth. A methodology wa developed from the laboratory data to predict head lo and reitance coefficient a a function of lope and depth. Input data can be collected from the field or etimated plant characteritic may be ued in the methodology. The evaluation of vegetative impact on propoed and exiting channel to determine flow capacity and water-urface elevation require proper hydraulic roughne value for hrub and other aethetically and environmentally deirable plant. Given the near complete lack of hydraulic roughne value for hrub and imilar vegetation, the accurate etimation of channel capacity and water-urface elevation ha previouly been difficult at bet. Detail of the tudy may be found in Freeman, Rahmeyer, and Copeland (in preparation). REITANCE COEFFICIENT: Reitance to flow i typically characterized by a roughne coefficient. The mot commonly ued equation for flow reitance i the Manning equation. The ratio of hear velocity to mean velocity, V * /V, i another form of reitance coefficient, and may be thought of a the ratio of hear tre to inertial force. All variable are defined in Appendix I. There are other reitance coefficient in ue including the Darcy-Weibach friction factor, f, and the Chezy C. Thee can all be converted eaily to Manning n. In thi tudy, reitance equation were developed for the hear velocity to average velocity ratio becaue it i dimenionle and ha a ound theoretical bai, and for the Manning coefficient, becaue it ue i widepread. The Manning reitance coefficient for vegetation i calculated in 1

2 ERDC/CL CETN-VIII-3 December 000 conformity with the Cowan (1956) method for additive reitance. Thi method conit of addition to roughne for variou urface irregularitie and vegetation. TIFFNE MODULU: The modulu of plant tiffne, E, i critical to the calculation of reitance becaue of the flexibility of the plant and the deformation of leaf mae due to the flow force. The modulu of plant tiffne i calculated by E F 45 F45 = = I D (1) The data neceary to ue Equation 1 i obtained by meauring the force, F 45, neceary to bend the plant to an angle of 45 deg. The 45-deg angle i meaured from the initial vertical poition to the tem or leaf ma at the point where the force i meaured i.e., at / a hown in Figure 1. / / D F 45 Figure 1. Methodology for meauring plant tiffne for calculating E in the field, for plant with effective height of leaf ma approximately equal to the plant height The reearch performed in the laboratory and in the field indicated that the tiffne modulu can be etimated from the relationhip of E to the ratio of /D (Equation ). Thi equation give the modulu in pound per quare foot, while Equation 3 give the value in newton per quare meter. E lbf ft = 1.597E D D D 3 () E ( N ) = 7.648E E E03 m D D D 3 (3)

3 ERDC/CL CETN-VIII-3 December 000 Actual field meaurement of E are recommended where poible. ince the tiffne modulu varie depending on the plant ize, it wa determined that if the calculated modulu for a particular plant ize wa divided by (/D ) 1.5, the tiffne modulu became independent of plant ize and one value could be ued for all plant ize. Meaured tiffne moduli for plant ued in the experimental tudy are reported in Freeman, Rahmeyer, and Copeland (in preparation). REITANCE EQUATION FOR UBMERGED VEGETATION: Reult from large flume experiment were analyzed to determine the regreion of variable for ubmerged vegetation. The analyi found that log and polynomial relationhip gave a poor data fit while a power relationhip had very good reult. The parameter in the equation were modified to allow a direct olution for reitance (for a given depth) by combining the original parameter with Manning equation and the equation for hear velocity. Thi modification and combination of equation reulted in Equation 4 for hear velocity and Equation 5 for Manning n. In thee equation the reitance coefficient repreent the combined reitance of the bed and the plant. Reitance coefficient due only to vegetation mut be determined by ubtracting the bed reitance. In thee experiment the Manning bed reitance coefficient wa found to be 0.0 and V * /V for the bed wa found to be V* V = g C E A = ρa iv* Y O 0.43 ( MA ) i 0.73 v V* R h (4) n = K n E A ρav i * Y O 0.43 v V* R V * 0.73 ( MA ) ( R ) / 3 ( ) 1/ i h h (5) It i important to note that the plant characteritic, A i, and A are the initial characteritic of the plant without the effect of flow ditortion. During the experiment, it wa oberved that ince the plant bent with flow, ubmergence occurred at flow depth le than 80 percent of the plant height. Equation 4 and 5 are to be applied only for ubmerged flow defined by Y o > 0.8. REITANCE EQUATION FOR PARTIALLY UBMERGED VEGETATION: Data for partially ubmerged vegetation were analyzed to determine the regreion of variable. The regreion analyi again found that a log relationhip gave a poor fit of data while a power relationhip produced very good reult. Equation 6 and 7 fit the data well and allow direct olution for reitance if the flow depth i known. ere again, in thee equation the reitance coefficient repreent the combined reitance of the bed and the plant. Reitance coefficient due only to vegetation mut be determined by ubtracting the bed reitance. In thee experiment the Manning bed reitance coefficient wa found to be 0.0 and V * /V for the bed wa found to be V* V = g C = E A * V* Rh 3.487E 05 ( ) * ρ MAi Ai V* υ (6) 3

4 ERDC/CL CETN-VIII-3 December 000 n = K n E A 3.487E 05 * ρ Ai V * ( ) 3 * V* R R / 1/ M A h h i ν V* (7) The blockage area in Equation 6 and 7 wa changed to an effective area, A i *, ince only a portion of the leaf ma produce blockage under partially ubmerged flow condition. CONCLUION: When plant were ubmerged, it wa oberved that the plant leaf ma tended to trail downtream forming a treamlined, almot teardrop-haped profile. The leaf ma hape changed with velocity and became more treamlined with increaing velocity. The effect of thi phenomenon wa a ignificant decreae in the drag coefficient and reitance coefficient with velocity. On the other hand, reitance increaed with depth for partially ubmerged plant a the blockage area increaed with depth until the plant were ubmerged. The tranition between ubmerged and partially ubmerged flow occurred at a depth of about 80 percent of the undeflected plant height. It wa alo oberved that the leaf ma or foliage canopy diverted flow beneath the canopy. The bottom flow reulted in ignificant velocitie along the channel bed cauing general cour and increaed ediment tranport. The bed velocitie were ufficient to tranport and move the larget ize of gravel found in the flume bed. The hydraulic roughne of a vegetated channel wa hown to be a function of the tiffne of the plant growing in the channel, the depth, velocity, and hydraulic radiu of the channel, plant denity, and frontal area of the plant obtructing the flow. It wa determined that the roughne can be calculated directly if the depth of flow i known. The modulu of plant tiffne, E, i critical to the calculation of reitance becaue of the flexibility of the plant and the deformation of leaf mae due to the flow force. The reearch performed in the laboratory and in the field indicated that the tiffne modulu can be etimated from the relationhip of E to the ratio of /D. Actual field meaurement of E are recommended where poible. The tiffne modulu can alo be etimated from meaured value of imilar plant. ince the tiffne modulu varie depending on the plant ize, it wa determined that if the calculated modulu for a particular plant ize wa divided by (/D ) 1.5, the tiffne modulu became independent of plant ize and one value could be ued for all plant ize. ADDITIONAL INFORMATION: For additional information contact Dr. Ronald R. Copeland, Coatal and ydraulic Laboratory, U.. Army Engineer Reearch and Development Center, 3909 all Ferry Road, Vickburg, M 39180, at or Ronald.R.Copeland@erdc.uace.army.mil. The content of thi TN are not to be ued for advertiing, publication, or promotional purpoe. Citation of trade name doe not contitute an official endorement or approval of the ue of uch commercial product. 4

5 ERDC/CL CETN-VIII-3 December 000 REFERENCE Cowan, W. (1956). Etimating hydraulic roughne coefficient, Agricultural Engineering, 37(7), Freeman, G. E., Rahmeyer, W.., and Copeland, R. R. (in preparation). Determination of reitance due to hrub and woody vegetation, Technical Report, U.. Army Engineer Reearch and Development Center, Vickburg, M. 5

6 ERDC/CL CETN-VIII-3 December 000 Appendix I: Lit of Variable Numerou variable are ued throughout Freeman, Rahmeyer, and Copeland (in preparation). Thoe variable and their definition are preented here. Figure I1 and I how the meaurement that define the variable involving the leaf ma and plant dimenion for ubmerged and emergent (unubmerged or partially ubmerged) flow condition. A Cro ectional flow area, ft or m² A i Frontal area of an individual plant blocking flow, approximated by the equivalent rectangular area of blockage by W e, ft or m² * A i A Net ubmerged frontal area of a partially ubmerged plant, ft or m² Total cro-ectional area of all of the tem() of an individual plant, meaured at /4, ft² or m² b Width of channel flume, ft or m C Chezy reitance coefficient, ft 1/ / or m 1/ / C D Drag coefficient of vegetation, dimenionle D tem diameter, meaured at a height of /4, ft or m E Exponential cientific notation E Modulu of plant tiffne, lbf/ft² or N/m² f Darcy-Weibach friction factor, dimenionle f b Friction factor for the bed and plant, dimenionle f w Friction factor for the wall, dimenionle The horizontal force neceary to bend a plant tem 45 deg, lbf or N F 45 F D F r g ' Drag force, lbf or N Froude number, dimenionle Acceleration due to gravity = 3.17 ft/ or m/² Average undeflected plant height, ft or m Undeflected height of the leaf ma of a plant, ft or m * Undeflected height of leaf ma that i below water urface for a partially ubmerged plant, ft or m (ee Figure I) I econd moment of inertia of cro ection of plant tem, ft 4 or m 4 K n Unit converion factor for Manning equation, ft 1/3 /ec or 1.0 m 1/3 /ec L Channel reach length, ft or m M Relative plant denity, number of plant per ft² or m² n Total Manning roughne coefficient, including idewall roughne 6

7 n b Manning reitance coefficient for vegetation and channel bed n veg Manning reitance coefficient for vegetation n o Manning reitance coefficient for the bed P Wetted perimeter, ft or m R e Reynold number, R e = V R h /ν R h ydraulic radiu, R h = flow area / wetted perimeter, ft or m R b ydraulic radiu for the bed and plant, ft or m R w ydraulic radiu for the wall, ft or m Bed or energy lope, dimenionle o Bed lope, dimenionle f Energy lope, dimenionle V Mean channel velocity, ft/ or m/ V P Local plant approach velocity in front of the leaf ma, ft/ or m/ V * hear velocity, V * = (g R h ) ½, ft/ or m/ V * /V Reitance coefficient, dimenionle Y o Flow depth, ft or m W e Equivalent average plant width, We = A i /, ft or m dy/dx Unit change in lope of the water urface γ pecific weight of water, lbf/ft 3 or N/m 3 ν Fluid dynamic vicoity, ft²/ or m²/ ρ Fluid denity, lug/ft 3 ( lbf-ec /ft 4 ) or kg/m 3 τ o hear tre on channel bottom, (τ o = γ R h ), lbf/ft or N/m² ERDC/CL CETN-VIII-3 December 000 7

8 ERDC/CL CETN-VIII-3 December 000 W e Y O D Figure I1. Plant dimenion definition for ubmerged plant Figure I. Plant dimenion definition for partially ubmerged plant 8