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Theoretical development Substituting eq 4 and 5 into eq 3 and rearranging At a well designed and operated overland flow terms, detention time can be calculated as follows: site, water flows downslope as a thin sheet until it ( 3 v W2 �1�3 freefalls into a runoff collection ditch. Under these = IL L. (6) conditions, the overland flow system operates in the ag S Q2 laminar flow regime (Kirkby 1978) where Reynolds numbers are less.than 500 (Streeter 1966). At the In more convenient terms with the average detention CRREL site Reynolds numbers ranged between 38 time described in minutes (T) and the average overland and 226, which is well within the laminar flow re- flow rate (q) in m3 hr-1 of width,eq 6 becomes gime. For the simplest case of laminar flow over a smooth surface, the average velocity vs can be de- T =5651'r vl (113 L 7) scribed by the following equation (Nakano 1978): . ogS1(3 g213 ' 2 Assuming a kinetic viscosity of 0.112 x 1U-1 m2 s' v =g Sd (m s 1) (1) (at 15.6 C) and substituting the value of the gravita- s P tional constant (9.81 m s ) eq 7 is reduced to where g=gravitational constant,9.81 m s2 L S=slope, mm' T =0.0274at/3S113g2f3 (8) d=average depth of flow, m Y= kinematic viscosity, m2 s'. Determination of resistance coefficient,a For an overland flow system, resistance to flow will To determine a,eq 8 was evaluated using detention be greater because of the grass and vegetative litter. time data obtained from the CRREL overland flow Therefore,the average overland flow velocity V will test site. For each CRREL test section, the values be lower than the smooth surface velocity vs and of L and S are 30.5 and 0.05 m m' respectively. can be expressed as Substituting these values,eq 8 becomes V=a vs (m 5-1) (2) T= 2.27 (9) a1/3 q2/3 where a is a resistance coefficient. Substituting eq 2 into 1, the velocity of flow over an overland flow By plotting detention time vs the average overland terrace can be calculated by flow rate on log-log paper,a can be determined from the line of bestfit. This was done for the CRREL V=a tg S d2] , where a< 1.0. (3) 3 data shown in Figure 5. A regression analysis indi- v sates good correlation (r=0.78) between application rate and detention time. However, the standard If one assumes that most of the water flows in deviation is large, indicating that detention time a relatively straight path downslope, the velocity varied considerably for a given overland flow rate. V can also be expressed as For example,at an application rate of 0.2 m' hr' m-1 of width, the predicted detention time is 34 V_ L (4) minutes. Within one standard deviation,detention I times could range from 23 to 48 minutes. Most of this deviation appears to be caused by a difference where L is the length of terrace in meters, and t in results obtained during the 1978 and 1979 growing the hydraulic detention time in seconds. seasons. Also,from the continuity equation, the average The detention times were generally higher in depth of flow of can be determined by 1979 than 1978 for the same overland flow rate. A possible explanation for this difference is an increase d Q t (5) in vegetation density during 1979 which caused an LW increase in resistance to flow. This conclusion is supported by the higher grass yields in 1979 than where Q is the average overland flow rate (m3 f') 1978 (Palazzo in prep.). Another reason for the and W the width of the terrace in meters. increased detention times could be the presence 5