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Shallow flow of water through non-submerged vegetation
Agricultural Water Management, 8 (1984) 375--385
375
Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands
S H A L L O W FLOW O F W A T E R T H R O U G H N O N - S U B M E R G E D
VEGETATION
A.K. TURNER 1 and N. CHANMEESRI 2 ~Agricultural Engineering Section, Department of Civil Engineering, University of Melbourne, Parkville, Vic. 3052 (Australia) 2 Thai Section, Radio Australia, Melbourne, Vic. (Australia)
(Accepted 25 April 1983)
ABSTRACT Turner, A.K. and Chanmeesri, N., 1984. Shallow flow of water through non-submerged vegetation. Agric. Water Manage., 8: 375--385. The shallow movement of water flowing through dense crops of wheat was studied for different crop densities and sowing patterns and ages. The common application of Manning's equation to such flows is shown to he inadequate, particularly since the flows can be described as mixed rather than turbulent. The more general discharge-depth equation has advantages for coping with the conditions, and relevant values of the parameters are provided both for (slope) °'s as well as for
a suggested(slope)°'3s INTRODUCTION T h e m o v e m e n t o f w a t e r t h r o u g h and over v e g e t a t i o n has b e e n studied m a i n l y f r o m t h e p o i n t o f view o f 'linings' f o r o p e n channels or grassed waterways. In such studies, t h e d e p t h o f w a t e r is usually greater t h a n t h e height o f t h e v e g e t a t i o n , which m i g h t be e r e c t or b e n t b y t h e flowing water. F o r various reasons, t h e r e has b e e n less emphasis o n t h e field s i t u a t i o n w h e r e t h e v e l o c i t y o f f l o w is small, so t h a t little d e f o r m a t i o n o f t h e v e g e t a t i o n might result. A listing o f papers related t o b o t h shallow and d e e p e r flows and veget a t i o n was given b y K o u w e n e t al. ( 1 9 7 9 ) .
Most irrigation water in south~east Australia is applied to pastures through border-check layouts. Because of the recent possibility of achieving accurate earthworks through laser-controlled machines, system design and operation is becoming more dominated by times of advance and recession. In turn, these times depend on the hydraulics of the shallow flow sheet. A n o t h e r e x a m p l e o f such flows relates t o t h e p u r i f i c a t i o n o f waste waters b y grass f i l t r a t i o n (overland flow). A f t e r p r i o r r e m o v a l o f solids, t h e w a t e r is e n a b l e d t o f l o w c o n t i n u o u s l y d o w n - s l o p e o v e r p r e p a r e d clay soils. T h e resistance o f f e r e d b y t h e soil and v e g e t a t i o n affects t h e h y d r a u l i c d e t e n t i o n t i m e , and also t h e o x i d a t i o n o f t h e e f f l u e n t b y t u r b u l e n c e . 0378-3774/84/$03.00
© 1984Elsevier Science Publishers B.V.
376 In both of these examples, the depth of water is usually less than about 75 mm, and the height of vegetation about 150 mm or more. Some aspects of this flow condition were reviewed in an earlier paper (Turner et al., 1978), where it was suggested that the discharge-depth equation for predicting velocity could offer better accuracy than the c o m m o n l y used Manning or Chezy equations. Manning's equation was originally developed for rivers in defined courses, and where the roughness elements did not basically intrude through the water stream. When applied to shallow flow over a wide, flat surface, it is usually written as: q = n -1 R s'3 S ''~
(1)
where q = discharge per unit width (1 m -1 s-I ); S = slope of the water surface (commonly assumed to be the same as the soil surface for long reaches, 11-1); n = the resistance term (contributed to by both soil and vegetation; called retardance by Ree and Palmer (1949) because of the much greater resistance offered by the vegetation); R = the hydraulic radius (mm) (assumed to be the same as depth for broad flat surfaces). When this equation is used for conditions much different than those for which it was proposed, there are problems in relation to n, R and the exponents for R and S. In their original work, Ree and Palmer (1949) plotted their results as 'n' versus the product of velocity and hydraulic radius taken together, although no rationale was advanced in support of this procedure. Their original work was done for submerged vegetation on relatively steep slopes (greater than 0.01), and the later work by Ree and Crow (1977) utilized the same type of graph to describe non-submerged, deep flows through tall crops growing on flatter surfaces. Kouwen et al. (1981) showed that there were problems with this approach, particularly for flat slopes, and advocated an alternative procedure based on 'n' and flexible stems for the vegetations. Most other research carried out for both deep and shallow flows has, in effect, adopted Manning's 'n', and attempts then made to define it better for the conditions that exist with vegetation. The difficulty with 'n' can be quickly realized since it varies markedly with depth, for shallow flows. Since it is within this range where the exampies of flow referrred to earlier are involved, 'n' values can be at the best unhelpful and even misleading. An example of this variability was given by Holden and Pilgrim (1978) for irrigation flows through pasture. The point is that values of 'n' can be obtained readily during field trials, whether or not equation (1) really applies. A typical graph of 'n' versus depth obtained from the experimental work to be described for a dense wheat crop is shown in Fig. 1 ; the problem of interpretation for shallow depths is obvious. In addition to the definition of resistance, there is the problem of hydraulic radius for these sub-divided flows. If R is the ratio of cross-sectional area to wetted perimeter, what allowance should be made for stems and leaves?
377 0.12
00 WHEAT (D
z
0.0B
×
x
z z
0.06
0.04
~IL 0.02
,
lo
2'0
1o
20
DEPTH {ram) Fig. 1. Manning's 'n' versus depth of flow for wheat crop at age 92 days and up to 800 mm tall, and showing the relative contributions of soil, stems and complete plants (flowering stage).
It is conceivable t h a t as the density of vegetative elements increases, the flow cross-section approaches a condition somewhat akin to porous media. Finally, the use of fixed e x p o n e n t for R (5/3 for Manning, 3/2 for the alternative Chezy), implies t h a t the flow sheet is always behaving in a fully turbulent condition. For the shallow flows of interest, it is more likely that the sheet condition is 'mixed', and changes back and forth between turbulent and laminar. Hence this fixed exponent of 5/3 is unlikely to be applicable, even if the vegetation might not have an effect on the exponent for slope (1/2). For these reasons, there seems to be little justification in making improvements or alterations to Manning's equation. As an alternative, there are two main procedures: (a) to develop a prediction equation based on the principles of hydrodynamics; (b) to develop a prediction equation based entirely on empirical procedures. In this paper, the approach (b) has been developed, and the same data will be reworked later, in regard to (a). SHALLOW FLOW T H R O U G H V E G E T A T I O N
The velocity of water moving over a soil surface and through a dense network of stems and leaves is generally slow, so that viscous shear can dominate rather than turbulent shear. This pattern can change during the life of a
378 plant (or crop) because the resistance offered by isolated seedlings will be much less than that of a mature crop or pasture. Hence the ratio of soil resistance to vegetative resistance changes during the growth cycle. There is a broad band of Reynolds numbers that denotes the presence of these mixed flows; the degree of mixing depends on the obstructions present and the degree of wake interference. For example, in the studies to be described, most of the Reynolds numbers were around 300, with the depth of flow used as the length parameter. (Even the use of depth in this manner is subject to question because of the volume occupied by the vegetation.) In an earlier paper, Turner et al. (1978) recommended the use of the discharge-depth equation as a likely basis for an empirical approach. This can be expressed as: q =ky
(2)
m
where q = discharge per unit width (1 m -1 s-l); y =depth of flow (mm); k = a parameter that provides for slope and roughness; m = an exponent that reflects the degree of mixing in the flow. Because of its flexibility, this equation can be used to describe a wide range of flows, and the values of k and m obtained from log-log plots of field data. In the above format, the effect of slope is built into k, and hence there is the problem of translating the results for the same vegetation, but to different slopes. In the earlier work, initial studies indicated that the inclusion of S °'s, as for Manning and Chezy, might be adequate. The equation can then be re-written as: q = G-l ym S0.s
(3)
where G is defined as a coefficient of roughness that is independent of slope, such that G = S °'s k -~ The test programme now to be described relates to equation (3), for a specific species. Wheat was selected as a crop that could be sown and grown under given patterns and densities. The stems are rigid, can be readily counted, and their diameters measured. It was intended to obtain this information to determine a possible 'vegetative index' that might be applicable at a later stage to the less definable condition of a clover-based pasture. EXPERIMENTAL
PROCEDURES
Wheat (vat. Kite) was grown in a relatively long concrete channel of fixed slope, and a smaller flume having a variable slope, located at the Mt. Derrim u t Field Station of the University of Melbourne. The channel had a length of 80 m and a rectangular cross-section 0.78 m wide by 0.45 m deep, with a longitudinal slope of 0.0010. The length was subdivided into eight sections, each 6 m long, by means of brick walls, so that there was a space of about 0.85 m between sections. A thin layer of crushed rock was laid above the floor and provided with frequent outlets for
379 internal drainage. A thickness of about 0.07 m of coarse sand was then placed over the rock to act as a filter, and loamy sand was placed over the sand to a depth of about 0.25 m, to form the bed for the experiments. Fig. 2 shows the general layout.
Y
u-U-J-~7 s P-T~
Fig. 2. Diagrammatic field view of equipment used.
Cultivation was done by a small rotary hoe when the soil was dry. In order to obtain uniform density for the soil in each section, about 0.1 m depth of water was maintained over the surface for about two weeks (i.e. the outlet drains were blocked); this practice also decreased the problem of weeds. While the soil was still wet, the surface was carefully graded, both laterally and longitudinally. The sequence of flooding, cutting and levelling was repeated twice in order to obtain the desired soil and surface conditions. Not all the weed seeds were killed by the flooding and, finally, methyl bromide gas was used under a plastic cover. After treatment, the flume was again flooded and drained. Because the channel was located in the open air, it was necessary to build a plastic greenhouse over it to reduce wind effects during the test period. Unfortunately this protective cover stimulated the growth of the vegetation. Water was applied to the upper end of the channel by a pump operating from a circulation storage and the discharge was measured through a standard orifice plate set in the delivery pipe. The distribution system provided for the water to be delivered to any one of the 'boxes' spaced between the test sections. Uniform flow in any one section was approximated as closely as possible by using a flap gate installed at the b o t t o m end of the section. The depths of water so regulated within a section were read at each of three stilling wells located outside the channel at that section. The zero readings for these wells were adjusted to match the level of the soil surface inside at t h a t location. The measurement of velocity profiles was attempted using nitrate injection with ion probes, but the electrodes used were too unstable. Maximum velocities were obtained using fine particles o f sawdust as floats on the water surface, and solubility traces from crystals of potassium permanganate gave an indication o f turbulence patterns.
380 T h e p l a c e m e n t o f seeds in the sections o f t h e channel is given in Table I. Hole-markers were used to enable t h e spacing to be c o n t r o l l e d and t h r e e seeds were p l a c e d in each hole. T h e g e r m i n a t i o n p e r c e n t a g e was 85%, which was higher t h a n t h a t o b t a i n e d in earlier checks o n germination. This explains t h e dense rate o f sowing, and later t h i n n i n g was impossible, since this w o u l d have spoilt t h e soil surface. A m i x e d t y p e o f fertilizer was applied at t h e t i m e o f sowing. TABLE I Placement patterns, spacings of seeds and bed slopes Test section
Spacing (m × m)
Grid pattern
Bed slope
A B
0.03 × 0.03 0.03 x 0.03
square diagonal
C
dense broadcast
random a
D E F G H
0.04 x 0.04 0.05 x 0.05 dense broadcast 0.04 x 0.04 0.05 x 0.05
square square random diagonal diagonal
0.0020 0.0020 0.0030 0.0025 0.0028 0.0030 0.0027 0.0028
aResults not used in this study.
Only o n e section was studied at any o n e time. T h e drainage outlets f o r t h a t section were t h e n b l o c k e d a n d the soil saturated. A f t e r u n i f o r m flows were established f o r the desired d e p t h s and times, the soil was drained to await t h e n e x t test period. A t o t a l o f eight t o t e n tests was r u n over each sect i o n o f the long c h a n n e l during t h e o n e season, t o c o v e r the d i f f e r e n t stages o f plant growth. T h e m a x i m u m d e p t h o f w a t e r used in this test series was a b o u t 100 m m . T h e variable-slope flume was 4.0 m long, 0.45 m wide, and 0.40 m deep. T h e ratios o f w i d t h to d e p t h studies were again > 5 and this was t a k e n as representing b r o a d f l o w with little side effects u n d e r c o n d i t i o n s o f dense vegetation. This f l u m e was fixed o n t o a steel f r a m e for tilting, and the discharge m e a s u r e m e n t s were also m a d e b y orifice plate. T h e test section was 2.5 m long. EXPERIMENTAL
RESULTS
Constant slope T h e general applicability o f the discharge-depth e q u a t i o n f o r these t y p e s o f shallow flow can be seen in Fig. 3, w h e r e a t y p i c a l test result for t w o o f t h e t r e a t m e n t s is shown. T h e ' p i c t u r e ' is similar t o t h o s e s h o w n in an earlier p a p e r ( T u r n e r et al., 1 9 7 8 ) .
381
6.0 4.0
SECTI
cg,o
2.0 W 0 OC -r
~n
1.0
0.6
I
10
I
20 DEPTH
I
40 {mrn}
I
I
60
100
Fig. 3. Discharge-depth plots for wheat at age 92 days for Sections B and H (constant slope).
The tests on the growing plants were carried o u t at 16, 37, 92, 121 and 162 days after sowing, respectively. For these tests, separate counts were taken of stems, and measurements made of stem diameter, temperatures and slopes of the water surface. During this test period, the water temperature ranged between 10 and 16°C, which caused a small variation in velocity due to viscosity effects of up to 2%. The effect of the volume of stems on the depth o f flow was likewise of the order of 2%, and over the test section the water surface was parallel to the bed surface to within one or t w o millimetres. Hence these effects were ignored subsequently. The depth of flow was assumed to be close to the hydraulic radius, and the effect of the sidewalls of the channel reduced b y the drag of the stems, leaves and stem hairs. The results for two of the treatments showing response to age of the plants are given in Table II, for the exponents and constants in equation (2) and (3). In these results, there is a substantial difference in the values obtained for m, as against the constant 1.67 used in equation (1). The values are close to the 1.00 exponent, in effect adopted for Darcy's law for porous media. In general, values of m increased with the age of the plants, whereas k decreased, and accordingly G increased.
382 TABLE II Variation of flow parameters w i t h stage of growth TreatSeeds ment per m 2 (ram X m m )
Age (days)
No. o f stems per m 2
Stem Vegediameter 'tative (mm) index
m
k
G
40 x 40 (square)
625
16 57 92 121 162
1650
1.84 2.39 2.62 2.66 2.72
3030 3940 4300 4390 4490
1.01 1.04 1.09 1.11 1.24
0.11 0.08 0.05 0.04 0.03
0.45 0.65 1.00 1.25 1.92
50 x 50 (square)
400
16 57 92 121 162
1020
1.94 2.42 2.88 2.90 2.88
1950 2460 2950 2960 2950
0.93 1.13 1.28 1.28 1.35
0.23 0.08 0.04 0.04 0.02
0.23 0.65 1.33 1.33 2.30
The vegetative i n d e x s h o w n in Table II is t a k e n as the n u m b e r o f stems per unit area o f bed (m 2) multiplied b y the m e a n d i a m e t e r ( m m ) o f the stems m e a s u r e d at a height o f 10 m m above t h e bed. It is n o t a true i n d e x o f f r o n t a l area o f t h e stems because d e p t h has n o t been included. It also does n o t take into a c c o u n t hairs o n the stems, n o r t h e presence o f dead leaves. These leaves were p r e s e n t in greater n u m b e r s for the higher stem densities, a n d possibly caused m o r e drag t h a n the stems. The index also ignores the e f f e c t o f surface t e n s i o n menisci a r o u n d each stem, b u t this effect was s h o w n to be small in a previous s t u d y ( T u r n e r et al., 1978). Despite the inadequacies o f such an index, the values o f m and G m o v e d c o n s i s t e n t l y with changes in t h e index. G
M
1.30
G
//~/M
2.00
/,,, ,/ //,"
1.10
1.00
1.00
J i i J 20 60 100 1/.0 N° OF DAYS AFTER SOWING
i 180
0.50
Fig. 4. Trend curves showing variation of G and m with age of wheat plants.
383
Because plants do not grow uniformly with age after sowing (especially during the winter season), a graph of G and m versus age can only show trends. Such a graph incorporating results from all tests is shown in Fig. 4. The results for the final test for all the treatments is shown in Table III. Since there seemed to be no obvious trend in these or the earlier tests, in regard to square or diagonal spacing, a mean value is also given for each spacing. TABLE
III
Sowing pattern, density a n d f l o w p a r a m e t e r s f o r m a t u r e p l a n t s Treatment
Seeds
(ram x ram)
per m 2
No. o f stems ( m -2 )
Stem diameter (mm)
Vegetative
m
k
G
index
30 x 3 0 (square)
1100
2190
1.69
3700
1.29
0.013
3.46
30 x 30 (diagonal)
1100
1650
2.72
4500
1.21
0.026
1.73
4050
1.25
0.020
2.60
30 × 30 (mean) 40 × 40 (square)
625
1650
2.72
4500
1.24
0.026
1.92
40 × 40 (diagonal)
625
1630
2.10
3400
1.34
0.013
4.00
3950
1.29
0.020
2.96
40 x 40 (mean) 50 × 50 (square)
400
1020
2.88
2950
1.35
0.023
2.30
50 X 5 0 (diagonal)
400
1020
2.89
2950
1.25
0.030
1.77
2950
1.30
0.027
2.04
50 x 50
(mean)
In general, as for Table II, the lower the vegetative index, the higher the value of m. The values for G are more irregular, and this could be due to the errors in determining these values from their respective graphs. The bed resistance contributed only a b o u t 10% of the total drag.
Variable slope Graphs of discharge versus depth for a single plant density and variable slope are shown in Fig. 5. The number of stems was 2200 per m 2, which
384 60
z,.o
"~u~
S
2.0
uJ cr :£.
• 0.0034 x 0.002 1.0
0.5
1'o
2'o
8'0 DEPTH
( mm
1;o
)
Fig. 5. Discharge-depth plots for mature wheat (variable slopes).
correspond to the 30 mm X 30 mm square spacing used in the fixed slope tests. The plants were mature, so that this study was not as comprehensive as for the o t h e r tests. In addition, the length of the test section for this flume was shorter than those for the fixed-slope tests. The range o f slopes studied was f r om 0.0017 to 0.0100. For these conditions, the values o f m, k and G are shown in Table IV. There does seem to TABLE IV Variation of flow parameters with slope Slope,
0.0017 0.0021 0.0034 0.0050 0.0067 0.0084 0.0100
s
m
1.20 1.20 1.22 1.24 1.28 1.30 1.30
k
0.015 0.016 0.017 0.019 0.020 0.021 0.023
S °'s k -1
S ° ' 3 S k-~
(G)
(J)
2.7 2.8 3.4 3.7 4.1 4.4 4.4
7.3 7.5 8.2 8.4 8.5 9.0 8.7
385 be a small effect of slope on m values, b u t a greater effect on G values. Hence, instead of G being taken as S °'s k -1 with the exponent of slope being 0.5, an alternative e x p o n e n t o f a b o u t 0.35 is shown in the table. The use of such an e x p o n e n t gave a nearly constant value for the resistance term, which will n o w be termed J. Hence this initial study indicates that an exponent of a b o u t 0.35 is preferable to the 0.5 term used in the Manning equation. CONCLUSIONS
The inadequacy of the Manning equation for describing shallow flow through dense vegetation is again demonstrated, and the more flexible discharge
The contribution of Mr. R.G. McIlroy, Senior Technical Officer, througho u t this study, is gratefully acknowledged.
REFERENCES Holden, G.W. and Pilgrim, D.H., 1978. A field study of border check irrigation. Proc. Agric. Eng. Conf. Inst. Eng. Aust., Toowoomba, Qld., pp. 225--228. Kouwen, N., Li, R. and Simons, D.B., 1979. A selected annotated bibliography on the effect of vegetation on flow resistance in open channels. Document p~-epared by Civil Engineering Department, Colorado State University, Fort Collins, CO, 28 pp. Kouwen, N., Li, R. and Simons, D.B., 1981. Flow resistance in vegetated waterways. Trans. ASAE, 24: 684--690, 698. Ree, W.O. and Crow, F.R., 1977. Friction factors for vegetated waterways of small slope. ARS-S-151, USDA Agricultural Research Service, Washington, DC, 50 7 ~Ree, W.O. and Palmer, V.J., 1949. Flow of water in channels protected by vegetated linings. Bull. 967, USDA Soil Conservation Service, Washington, DC, 115 pp. Turner, A.K., Langford, K.J., Myo Win and Clift, T.R., 1978. Discharge-depth equation for shallow flow. Proc. ASCE, 104 (IR1): 95--110.
375
Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands
S H A L L O W FLOW O F W A T E R T H R O U G H N O N - S U B M E R G E D
VEGETATION
A.K. TURNER 1 and N. CHANMEESRI 2 ~Agricultural Engineering Section, Department of Civil Engineering, University of Melbourne, Parkville, Vic. 3052 (Australia) 2 Thai Section, Radio Australia, Melbourne, Vic. (Australia)
(Accepted 25 April 1983)
ABSTRACT Turner, A.K. and Chanmeesri, N., 1984. Shallow flow of water through non-submerged vegetation. Agric. Water Manage., 8: 375--385. The shallow movement of water flowing through dense crops of wheat was studied for different crop densities and sowing patterns and ages. The common application of Manning's equation to such flows is shown to he inadequate, particularly since the flows can be described as mixed rather than turbulent. The more general discharge-depth equation has advantages for coping with the conditions, and relevant values of the parameters are provided both for (slope) °'s as well as for
a suggested(slope)°'3s INTRODUCTION T h e m o v e m e n t o f w a t e r t h r o u g h and over v e g e t a t i o n has b e e n studied m a i n l y f r o m t h e p o i n t o f view o f 'linings' f o r o p e n channels or grassed waterways. In such studies, t h e d e p t h o f w a t e r is usually greater t h a n t h e height o f t h e v e g e t a t i o n , which m i g h t be e r e c t or b e n t b y t h e flowing water. F o r various reasons, t h e r e has b e e n less emphasis o n t h e field s i t u a t i o n w h e r e t h e v e l o c i t y o f f l o w is small, so t h a t little d e f o r m a t i o n o f t h e v e g e t a t i o n might result. A listing o f papers related t o b o t h shallow and d e e p e r flows and veget a t i o n was given b y K o u w e n e t al. ( 1 9 7 9 ) .
Most irrigation water in south~east Australia is applied to pastures through border-check layouts. Because of the recent possibility of achieving accurate earthworks through laser-controlled machines, system design and operation is becoming more dominated by times of advance and recession. In turn, these times depend on the hydraulics of the shallow flow sheet. A n o t h e r e x a m p l e o f such flows relates t o t h e p u r i f i c a t i o n o f waste waters b y grass f i l t r a t i o n (overland flow). A f t e r p r i o r r e m o v a l o f solids, t h e w a t e r is e n a b l e d t o f l o w c o n t i n u o u s l y d o w n - s l o p e o v e r p r e p a r e d clay soils. T h e resistance o f f e r e d b y t h e soil and v e g e t a t i o n affects t h e h y d r a u l i c d e t e n t i o n t i m e , and also t h e o x i d a t i o n o f t h e e f f l u e n t b y t u r b u l e n c e . 0378-3774/84/$03.00
© 1984Elsevier Science Publishers B.V.
376 In both of these examples, the depth of water is usually less than about 75 mm, and the height of vegetation about 150 mm or more. Some aspects of this flow condition were reviewed in an earlier paper (Turner et al., 1978), where it was suggested that the discharge-depth equation for predicting velocity could offer better accuracy than the c o m m o n l y used Manning or Chezy equations. Manning's equation was originally developed for rivers in defined courses, and where the roughness elements did not basically intrude through the water stream. When applied to shallow flow over a wide, flat surface, it is usually written as: q = n -1 R s'3 S ''~
(1)
where q = discharge per unit width (1 m -1 s-I ); S = slope of the water surface (commonly assumed to be the same as the soil surface for long reaches, 11-1); n = the resistance term (contributed to by both soil and vegetation; called retardance by Ree and Palmer (1949) because of the much greater resistance offered by the vegetation); R = the hydraulic radius (mm) (assumed to be the same as depth for broad flat surfaces). When this equation is used for conditions much different than those for which it was proposed, there are problems in relation to n, R and the exponents for R and S. In their original work, Ree and Palmer (1949) plotted their results as 'n' versus the product of velocity and hydraulic radius taken together, although no rationale was advanced in support of this procedure. Their original work was done for submerged vegetation on relatively steep slopes (greater than 0.01), and the later work by Ree and Crow (1977) utilized the same type of graph to describe non-submerged, deep flows through tall crops growing on flatter surfaces. Kouwen et al. (1981) showed that there were problems with this approach, particularly for flat slopes, and advocated an alternative procedure based on 'n' and flexible stems for the vegetations. Most other research carried out for both deep and shallow flows has, in effect, adopted Manning's 'n', and attempts then made to define it better for the conditions that exist with vegetation. The difficulty with 'n' can be quickly realized since it varies markedly with depth, for shallow flows. Since it is within this range where the exampies of flow referrred to earlier are involved, 'n' values can be at the best unhelpful and even misleading. An example of this variability was given by Holden and Pilgrim (1978) for irrigation flows through pasture. The point is that values of 'n' can be obtained readily during field trials, whether or not equation (1) really applies. A typical graph of 'n' versus depth obtained from the experimental work to be described for a dense wheat crop is shown in Fig. 1 ; the problem of interpretation for shallow depths is obvious. In addition to the definition of resistance, there is the problem of hydraulic radius for these sub-divided flows. If R is the ratio of cross-sectional area to wetted perimeter, what allowance should be made for stems and leaves?
377 0.12
00 WHEAT (D
z
0.0B
×
x
z z
0.06
0.04
~IL 0.02
,
lo
2'0
1o
20
DEPTH {ram) Fig. 1. Manning's 'n' versus depth of flow for wheat crop at age 92 days and up to 800 mm tall, and showing the relative contributions of soil, stems and complete plants (flowering stage).
It is conceivable t h a t as the density of vegetative elements increases, the flow cross-section approaches a condition somewhat akin to porous media. Finally, the use of fixed e x p o n e n t for R (5/3 for Manning, 3/2 for the alternative Chezy), implies t h a t the flow sheet is always behaving in a fully turbulent condition. For the shallow flows of interest, it is more likely that the sheet condition is 'mixed', and changes back and forth between turbulent and laminar. Hence this fixed exponent of 5/3 is unlikely to be applicable, even if the vegetation might not have an effect on the exponent for slope (1/2). For these reasons, there seems to be little justification in making improvements or alterations to Manning's equation. As an alternative, there are two main procedures: (a) to develop a prediction equation based on the principles of hydrodynamics; (b) to develop a prediction equation based entirely on empirical procedures. In this paper, the approach (b) has been developed, and the same data will be reworked later, in regard to (a). SHALLOW FLOW T H R O U G H V E G E T A T I O N
The velocity of water moving over a soil surface and through a dense network of stems and leaves is generally slow, so that viscous shear can dominate rather than turbulent shear. This pattern can change during the life of a
378 plant (or crop) because the resistance offered by isolated seedlings will be much less than that of a mature crop or pasture. Hence the ratio of soil resistance to vegetative resistance changes during the growth cycle. There is a broad band of Reynolds numbers that denotes the presence of these mixed flows; the degree of mixing depends on the obstructions present and the degree of wake interference. For example, in the studies to be described, most of the Reynolds numbers were around 300, with the depth of flow used as the length parameter. (Even the use of depth in this manner is subject to question because of the volume occupied by the vegetation.) In an earlier paper, Turner et al. (1978) recommended the use of the discharge-depth equation as a likely basis for an empirical approach. This can be expressed as: q =ky
(2)
m
where q = discharge per unit width (1 m -1 s-l); y =depth of flow (mm); k = a parameter that provides for slope and roughness; m = an exponent that reflects the degree of mixing in the flow. Because of its flexibility, this equation can be used to describe a wide range of flows, and the values of k and m obtained from log-log plots of field data. In the above format, the effect of slope is built into k, and hence there is the problem of translating the results for the same vegetation, but to different slopes. In the earlier work, initial studies indicated that the inclusion of S °'s, as for Manning and Chezy, might be adequate. The equation can then be re-written as: q = G-l ym S0.s
(3)
where G is defined as a coefficient of roughness that is independent of slope, such that G = S °'s k -~ The test programme now to be described relates to equation (3), for a specific species. Wheat was selected as a crop that could be sown and grown under given patterns and densities. The stems are rigid, can be readily counted, and their diameters measured. It was intended to obtain this information to determine a possible 'vegetative index' that might be applicable at a later stage to the less definable condition of a clover-based pasture. EXPERIMENTAL
PROCEDURES
Wheat (vat. Kite) was grown in a relatively long concrete channel of fixed slope, and a smaller flume having a variable slope, located at the Mt. Derrim u t Field Station of the University of Melbourne. The channel had a length of 80 m and a rectangular cross-section 0.78 m wide by 0.45 m deep, with a longitudinal slope of 0.0010. The length was subdivided into eight sections, each 6 m long, by means of brick walls, so that there was a space of about 0.85 m between sections. A thin layer of crushed rock was laid above the floor and provided with frequent outlets for
379 internal drainage. A thickness of about 0.07 m of coarse sand was then placed over the rock to act as a filter, and loamy sand was placed over the sand to a depth of about 0.25 m, to form the bed for the experiments. Fig. 2 shows the general layout.
Y
u-U-J-~7 s P-T~
Fig. 2. Diagrammatic field view of equipment used.
Cultivation was done by a small rotary hoe when the soil was dry. In order to obtain uniform density for the soil in each section, about 0.1 m depth of water was maintained over the surface for about two weeks (i.e. the outlet drains were blocked); this practice also decreased the problem of weeds. While the soil was still wet, the surface was carefully graded, both laterally and longitudinally. The sequence of flooding, cutting and levelling was repeated twice in order to obtain the desired soil and surface conditions. Not all the weed seeds were killed by the flooding and, finally, methyl bromide gas was used under a plastic cover. After treatment, the flume was again flooded and drained. Because the channel was located in the open air, it was necessary to build a plastic greenhouse over it to reduce wind effects during the test period. Unfortunately this protective cover stimulated the growth of the vegetation. Water was applied to the upper end of the channel by a pump operating from a circulation storage and the discharge was measured through a standard orifice plate set in the delivery pipe. The distribution system provided for the water to be delivered to any one of the 'boxes' spaced between the test sections. Uniform flow in any one section was approximated as closely as possible by using a flap gate installed at the b o t t o m end of the section. The depths of water so regulated within a section were read at each of three stilling wells located outside the channel at that section. The zero readings for these wells were adjusted to match the level of the soil surface inside at t h a t location. The measurement of velocity profiles was attempted using nitrate injection with ion probes, but the electrodes used were too unstable. Maximum velocities were obtained using fine particles o f sawdust as floats on the water surface, and solubility traces from crystals of potassium permanganate gave an indication o f turbulence patterns.
380 T h e p l a c e m e n t o f seeds in the sections o f t h e channel is given in Table I. Hole-markers were used to enable t h e spacing to be c o n t r o l l e d and t h r e e seeds were p l a c e d in each hole. T h e g e r m i n a t i o n p e r c e n t a g e was 85%, which was higher t h a n t h a t o b t a i n e d in earlier checks o n germination. This explains t h e dense rate o f sowing, and later t h i n n i n g was impossible, since this w o u l d have spoilt t h e soil surface. A m i x e d t y p e o f fertilizer was applied at t h e t i m e o f sowing. TABLE I Placement patterns, spacings of seeds and bed slopes Test section
Spacing (m × m)
Grid pattern
Bed slope
A B
0.03 × 0.03 0.03 x 0.03
square diagonal
C
dense broadcast
random a
D E F G H
0.04 x 0.04 0.05 x 0.05 dense broadcast 0.04 x 0.04 0.05 x 0.05
square square random diagonal diagonal
0.0020 0.0020 0.0030 0.0025 0.0028 0.0030 0.0027 0.0028
aResults not used in this study.
Only o n e section was studied at any o n e time. T h e drainage outlets f o r t h a t section were t h e n b l o c k e d a n d the soil saturated. A f t e r u n i f o r m flows were established f o r the desired d e p t h s and times, the soil was drained to await t h e n e x t test period. A t o t a l o f eight t o t e n tests was r u n over each sect i o n o f the long c h a n n e l during t h e o n e season, t o c o v e r the d i f f e r e n t stages o f plant growth. T h e m a x i m u m d e p t h o f w a t e r used in this test series was a b o u t 100 m m . T h e variable-slope flume was 4.0 m long, 0.45 m wide, and 0.40 m deep. T h e ratios o f w i d t h to d e p t h studies were again > 5 and this was t a k e n as representing b r o a d f l o w with little side effects u n d e r c o n d i t i o n s o f dense vegetation. This f l u m e was fixed o n t o a steel f r a m e for tilting, and the discharge m e a s u r e m e n t s were also m a d e b y orifice plate. T h e test section was 2.5 m long. EXPERIMENTAL
RESULTS
Constant slope T h e general applicability o f the discharge-depth e q u a t i o n f o r these t y p e s o f shallow flow can be seen in Fig. 3, w h e r e a t y p i c a l test result for t w o o f t h e t r e a t m e n t s is shown. T h e ' p i c t u r e ' is similar t o t h o s e s h o w n in an earlier p a p e r ( T u r n e r et al., 1 9 7 8 ) .
381
6.0 4.0
SECTI
cg,o
2.0 W 0 OC -r
~n
1.0
0.6
I
10
I
20 DEPTH
I
40 {mrn}
I
I
60
100
Fig. 3. Discharge-depth plots for wheat at age 92 days for Sections B and H (constant slope).
The tests on the growing plants were carried o u t at 16, 37, 92, 121 and 162 days after sowing, respectively. For these tests, separate counts were taken of stems, and measurements made of stem diameter, temperatures and slopes of the water surface. During this test period, the water temperature ranged between 10 and 16°C, which caused a small variation in velocity due to viscosity effects of up to 2%. The effect of the volume of stems on the depth o f flow was likewise of the order of 2%, and over the test section the water surface was parallel to the bed surface to within one or t w o millimetres. Hence these effects were ignored subsequently. The depth of flow was assumed to be close to the hydraulic radius, and the effect of the sidewalls of the channel reduced b y the drag of the stems, leaves and stem hairs. The results for two of the treatments showing response to age of the plants are given in Table II, for the exponents and constants in equation (2) and (3). In these results, there is a substantial difference in the values obtained for m, as against the constant 1.67 used in equation (1). The values are close to the 1.00 exponent, in effect adopted for Darcy's law for porous media. In general, values of m increased with the age of the plants, whereas k decreased, and accordingly G increased.
382 TABLE II Variation of flow parameters w i t h stage of growth TreatSeeds ment per m 2 (ram X m m )
Age (days)
No. o f stems per m 2
Stem Vegediameter 'tative (mm) index
m
k
G
40 x 40 (square)
625
16 57 92 121 162
1650
1.84 2.39 2.62 2.66 2.72
3030 3940 4300 4390 4490
1.01 1.04 1.09 1.11 1.24
0.11 0.08 0.05 0.04 0.03
0.45 0.65 1.00 1.25 1.92
50 x 50 (square)
400
16 57 92 121 162
1020
1.94 2.42 2.88 2.90 2.88
1950 2460 2950 2960 2950
0.93 1.13 1.28 1.28 1.35
0.23 0.08 0.04 0.04 0.02
0.23 0.65 1.33 1.33 2.30
The vegetative i n d e x s h o w n in Table II is t a k e n as the n u m b e r o f stems per unit area o f bed (m 2) multiplied b y the m e a n d i a m e t e r ( m m ) o f the stems m e a s u r e d at a height o f 10 m m above t h e bed. It is n o t a true i n d e x o f f r o n t a l area o f t h e stems because d e p t h has n o t been included. It also does n o t take into a c c o u n t hairs o n the stems, n o r t h e presence o f dead leaves. These leaves were p r e s e n t in greater n u m b e r s for the higher stem densities, a n d possibly caused m o r e drag t h a n the stems. The index also ignores the e f f e c t o f surface t e n s i o n menisci a r o u n d each stem, b u t this effect was s h o w n to be small in a previous s t u d y ( T u r n e r et al., 1978). Despite the inadequacies o f such an index, the values o f m and G m o v e d c o n s i s t e n t l y with changes in t h e index. G
M
1.30
G
//~/M
2.00
/,,, ,/ //,"
1.10
1.00
1.00
J i i J 20 60 100 1/.0 N° OF DAYS AFTER SOWING
i 180
0.50
Fig. 4. Trend curves showing variation of G and m with age of wheat plants.
383
Because plants do not grow uniformly with age after sowing (especially during the winter season), a graph of G and m versus age can only show trends. Such a graph incorporating results from all tests is shown in Fig. 4. The results for the final test for all the treatments is shown in Table III. Since there seemed to be no obvious trend in these or the earlier tests, in regard to square or diagonal spacing, a mean value is also given for each spacing. TABLE
III
Sowing pattern, density a n d f l o w p a r a m e t e r s f o r m a t u r e p l a n t s Treatment
Seeds
(ram x ram)
per m 2
No. o f stems ( m -2 )
Stem diameter (mm)
Vegetative
m
k
G
index
30 x 3 0 (square)
1100
2190
1.69
3700
1.29
0.013
3.46
30 x 30 (diagonal)
1100
1650
2.72
4500
1.21
0.026
1.73
4050
1.25
0.020
2.60
30 × 30 (mean) 40 × 40 (square)
625
1650
2.72
4500
1.24
0.026
1.92
40 × 40 (diagonal)
625
1630
2.10
3400
1.34
0.013
4.00
3950
1.29
0.020
2.96
40 x 40 (mean) 50 × 50 (square)
400
1020
2.88
2950
1.35
0.023
2.30
50 X 5 0 (diagonal)
400
1020
2.89
2950
1.25
0.030
1.77
2950
1.30
0.027
2.04
50 x 50
(mean)
In general, as for Table II, the lower the vegetative index, the higher the value of m. The values for G are more irregular, and this could be due to the errors in determining these values from their respective graphs. The bed resistance contributed only a b o u t 10% of the total drag.
Variable slope Graphs of discharge versus depth for a single plant density and variable slope are shown in Fig. 5. The number of stems was 2200 per m 2, which
384 60
z,.o
"~u~
S
2.0
uJ cr :£.
• 0.0034 x 0.002 1.0
0.5
1'o
2'o
8'0 DEPTH
( mm
1;o
)
Fig. 5. Discharge-depth plots for mature wheat (variable slopes).
correspond to the 30 mm X 30 mm square spacing used in the fixed slope tests. The plants were mature, so that this study was not as comprehensive as for the o t h e r tests. In addition, the length of the test section for this flume was shorter than those for the fixed-slope tests. The range o f slopes studied was f r om 0.0017 to 0.0100. For these conditions, the values o f m, k and G are shown in Table IV. There does seem to TABLE IV Variation of flow parameters with slope Slope,
0.0017 0.0021 0.0034 0.0050 0.0067 0.0084 0.0100
s
m
1.20 1.20 1.22 1.24 1.28 1.30 1.30
k
0.015 0.016 0.017 0.019 0.020 0.021 0.023
S °'s k -1
S ° ' 3 S k-~
(G)
(J)
2.7 2.8 3.4 3.7 4.1 4.4 4.4
7.3 7.5 8.2 8.4 8.5 9.0 8.7
385 be a small effect of slope on m values, b u t a greater effect on G values. Hence, instead of G being taken as S °'s k -1 with the exponent of slope being 0.5, an alternative e x p o n e n t o f a b o u t 0.35 is shown in the table. The use of such an e x p o n e n t gave a nearly constant value for the resistance term, which will n o w be termed J. Hence this initial study indicates that an exponent of a b o u t 0.35 is preferable to the 0.5 term used in the Manning equation. CONCLUSIONS
The inadequacy of the Manning equation for describing shallow flow through dense vegetation is again demonstrated, and the more flexible discharge
The contribution of Mr. R.G. McIlroy, Senior Technical Officer, througho u t this study, is gratefully acknowledged.
REFERENCES Holden, G.W. and Pilgrim, D.H., 1978. A field study of border check irrigation. Proc. Agric. Eng. Conf. Inst. Eng. Aust., Toowoomba, Qld., pp. 225--228. Kouwen, N., Li, R. and Simons, D.B., 1979. A selected annotated bibliography on the effect of vegetation on flow resistance in open channels. Document p~-epared by Civil Engineering Department, Colorado State University, Fort Collins, CO, 28 pp. Kouwen, N., Li, R. and Simons, D.B., 1981. Flow resistance in vegetated waterways. Trans. ASAE, 24: 684--690, 698. Ree, W.O. and Crow, F.R., 1977. Friction factors for vegetated waterways of small slope. ARS-S-151, USDA Agricultural Research Service, Washington, DC, 50 7 ~Ree, W.O. and Palmer, V.J., 1949. Flow of water in channels protected by vegetated linings. Bull. 967, USDA Soil Conservation Service, Washington, DC, 115 pp. Turner, A.K., Langford, K.J., Myo Win and Clift, T.R., 1978. Discharge-depth equation for shallow flow. Proc. ASCE, 104 (IR1): 95--110.