THE INFLUENCE OF A THIN WATER LAYER ON WATERDROP IMPACT FORCES (*)

Transcription

1 THE INFLUENCE OF A THIN WATER LAYER ON WATERDROP IMPACT FORCES () Robert S. PALMER ( ) Agricultural Engineer, Soil and Water Conservation Research Division, Agricultural Research Service, U.S. Department of Agriculture, and Adjunct Professor of Agricultural Engineering, University of New Hampshire RÉSUMÉ Un appareil à mesure de contraintes a été utilisé pour mesurer directement la force d'impact des gouttes d'eau. Des relations contraintes-déformations montrent que les forces d'impact augmentent quand la couche d'eau est faite plus profonde, jusqu'à ce que la couche d'eau atteigne une profondeur critique. Quand la profondeur de l'eau dépasse cette profondeur critique, la force d'impact décroît jusqu'à une valeur qui vaut approximativement celle sans couche d'eau. Des études similaires ont été faites en utilisant des bassines remplies d'un sol fait de vase, d'argile et de limon. Les productions des déformations maxima avec perte du sol maximum sont en relation avec la même profondeur de la couche d'eau. Ces relations montrent qu'une mince couche d'eau augmente la force d'impact des gouttes d'eau et provoque des pertes de sol plus grandes que celles qui se produiraient sans l'existence de la couche d'eau. ABSTRACT A strain gage apparatus was used to measure directly the force of impact of waterdrops. Stress-drop mass relationships show that the impact force increases as the water layer is made deeper, until the water layer reaches some critical depth. As the depth of water is increased beyond this critical depth, the force of impact decreases until a strain value is reached, which approximates conditions without a water layer. Similar studies were conducted using cans filled with a silty clay loam soil. The occurrences of maximum strain and maximum soil loss are related to the same depth of water layer. This investigation shows that a thin water layer can increase the force of impact of waterdrops and cause greater soil losses than would occur if a thin water layer was not present. Several investigators () have demonstrated the efficacy of raindrops in loosening and splashing particles from the soil surface. Measurements of soil loss and splash resulting from raindrop impact forces show that maximum splash occurs shortly after the soil surface is wetted. Splash angles also increase (become more normal to the surface) with greater depths of water layers. A water layer on the soil surface obviously influences raindrop impact forces. The theoretical aspects of a solid sphere impacting on a liquid surface are discussed by Richardson (3) (). One theory, based on the conservation of momentum, assumes that the sudden reduction in the velocity ofa body with mass, A/, as it strikes a liquid surface, is caused by an apparent addition to its mass by the mass of the liquid, m, () Contribution from the Soil and Water Conservation Research Division, Agricultural Research Service, USDA, in cooperation with the New Hampshire Agricultural Experiment Station. ()Agricultural Engineer, USDA, Durham, New Hampshire, and Adjunct Professor of Agricultural Engineering, University of New Hampshire, Durham, New Hampshire. ( ) For a review of previous studies, see "Raindrop Erosion", by D. D. Smith and W. H. Wischmeier, Advances in Agronomy, Vol. 14, pp , 192. () Numbers in parentheses refer to appended references. 141

2 set instantaneously in motion. Thus, if VQ is the velocity just before impact, and V\ y just after : M V a = (M -I- m) V y The value of m for a solid sphere is half of its volume. This paper reports a laboratory study of drop impact forces as they are affected by a water layer above two different types of reference planes. A strain gage was incorporated into the first reference plane, and direct strain readings were made. The second reference plane was a soil surface from which the amount of soil loss was measured. There arc a number of limitations to this study. For example, the terminal velocity of the waterdrops was not achieved, as the height of drop fall was 0 inches. The synthetic raindrops produced in the laboratory were isolated ; that is, they were sufficiently spaced in time to assure static conditions on the reference plane. Natural rainstorms produce drops that fall in discordant patterns, and with a quantity of drops, that was not duplicated in this study. Even with these limitations, this study indicates that a water layer is an important factor in the splash erosion process. 1. APPARATUS AND PROCEDURE USING STRAIN GAGE The apparatus consists of a drop-forming device, a reference plane, a sensing clement, and recording equipment as shown in figure 1 (1). Drop forming was accomplished by passing water through small metal tubes. A 1-inch length of 3/-inch-diameter copper tubing stuffed with cotton produced a 5.9 mm average nominal diameter drop under a 10-inch head. The drops weighed APPARATUS FOR THE MEASUREMENT OF DROP IVPACT FORCE DROP FORMING DEVICE STRAIN GAGE AMPLIFIER and RECORDER OSCILLOGRAPH and CAMERA Fig

3 ± 0.00 grams. Using the same head, a 23 to 10 graded tube () stuffed with cotton at the outlet, produced a 4.7-mm average nominal diameter drop. The drops weighed ± grams. A 1.5-cm length of 23-gage stainless steel tubing produced drops with average nominal diameters of 2.9 mm under a 4.1-inch head. The drops weighed ± grams. The selected tube for a given test run was placed within a septum fitted into the bottom of a 3-foot water column, where the head was varied as desired. Before each test run, a 10 drop sample was taken to assure replicate drop sizes. As drops formed under a head of water, they passed into a 1 1/4- inch-diameter plastic tube 0 inches long that shielded them from air movements. The reference plane was made by gluing a soft rubber membrane over a 1 1/4- inch-high, hollow, truncated cone. The cone had a 1 1/2-inch top diameter. It was set into the bottom of a 10-inch pan having a 3 1/2-inch depth. The sensing clement consisted of a 1/2-inch spiral-type foil strain gage, glued to the underside of the membrane. The leads were connected to a strain gage amplifier. The strain gage amplifier passed the impact signal of the drop striking the strain gage into an oscilloscope, where the signal was photographed. The strain was then calculated using the formula (2) A SI S = F where e is the strain, R is the gage resistance (120 ohms), and Fis the gage factor (2.0). The change in resistance was determined by measuring the maximum amplitude of the signal photographed on the oscilloscope grid for a given test run. The stress values were read from a calibration curve. The data for the calibration curve was determined by plotting stress in gm/cm 2 versus strain in cm/cm under various static loads. The average drop weight was determined by dividing the number of drops formed into the weight of the issue collected during a set time-interval. The height of water in the water column was established at a specific height and re-established between successive test runs to assure duplication of drop size. The average nominal drop diameter was calculated from the weight. The nominal drop diameter is the diameter of a a drop whose spherical volume contains the weight of water in a given drop. Tests were run on nine different depths of water layers, 0, 2, 4,,, 10, 15, 20, and 30 mm above the strain gage, using drops with average nominal drop diameters of 5.9, 4.7, and 2.9 mm. Each set of conditions was replicated five times. The height of the water layer above the reference plane was established at the beginning of each test run, using a point gage. 2. RESULTS USING STRAIN GAGE Stress drop mass relationships are shown in figure 2 for each treatment. A factorial analysis of the treatments shown on page 144 indicates that significant differences occur in strain measurements for both drop diameters and water layers as well as for the interaction between these variables. The critical depth of the water layer for a particular waterdrop is the depth that causes the maximum strain. Figure 2 shows that the critical depths of water layer for drops with average nominal diameters of 5.9, 4.7, and 2.9 mm are, 4, and 2 mm, respectively. Under the conditions described, a water depth of about 20 mm approximates the situation without a water layer. Greater depths cushion or absorb an increasing proportion of drop impact forces. The difference in strain values when no water layer was above the gage and the strain induced at the critical depth does not increase proportionally with increased drop mass, as shown on page 144. () A 23 to 10 graded tube is made of 1.5-cm lengths of 23, 19, 1, 13, and 10-gage stainless steel tubing soldered together. 143

4 STRESS-DROP MASS RELATIONSHIP FOR VARIOUS DEPTHS OF WATER LAYERS DROP MASS, grams Fig. 2 FACTORIAL ANALYSIS.1095 Source of Variation Degrees of Freedom Mean Square "F" Values Treatment Effects : Drop Diameter Water Layer Drop Diameter and Water Layer ( ) ( ) (). ()Statistical significance at 0.01 level. The medium size drop is about four times heavier, and the large drop is about eight and one-half times heavier, than the small drop. Yet the difference in strain between no water layer and the critical depth increases about three-fold above that of the small drop for both of the heavier drops. 144

5 Drop Mass Times Larger Mass Than Small Drop Strain at Critical Depth Minus Strain With No Water Layer Times Greater Difference in Strain gm cm/cm APPARATUS AND PROCEDURE USING SOIL CANS Using the drop-forming apparatus previously described, drops with average nominal diameters of 5.9, 4.7, 2.9 mm were allowed to fall 0 inches onto the surface of a standard 5.4-mm-diameter soil can tilled with SufTîeld silty clay loam soil. The mechanical analysis for this soil is shown below. Particle Size Percent Sand particles, I to 0.05 mm 7 Silt particles, 0.05 to mm 55 Clay particles, smaller than mm 3 Before each test run, a 10 drop sample was taken to assure replicate drop sizes. Nine depths of water layers, 0, 2, 4,,, 10, 15, 20, and 30 mm above the soil sample were replicated eight times for each test run of 100 drops. The test samples were placed in a bucket provided with an overflow tube to control the level of water above the surface of the soil in the can. To assure replicate soil surfaces, each sample was prepared in the following manner. Sufficient water was added to an air-dried quantity of soil to bring the soil moisture content to about 25 percent. This pasty mixture was packed into a soil can until the soil and can weighed just over 10 grams when the top was smoothed. The cans were then put under water for two hours. Upon removal from the water bath, they were dried for 5 minutes at 120 F. with the cover on the can to remove the moisture from the outside of the can. The wet volume weight was it.04 gm/cc. The moisture content of the soil after treatment was 23. ~ 2.1 percent. The soil cans were carefully weighed before and after testing to determine the amount of soil loss due to splash erosion. Comparisons were made to determine if the soil loss values under each of nine different water layers were analogous to the data taken with the strain gage reference plane. After each treatment, the sample was photographed and the depth of the hole, or depression formed was measured. An outline of the depression formed for a given treatment was made using a vertical sketch master, and planimetric measurement was made to determine the surface area of the depression. 4. RESULTS USING SOIL CANS An analysis of variance was made of the amount of soil loss using 100 drops of the drop diameters and nine water layers. As shown below, differences in soil loss 145

6 among drop diameters and water layers were statistically significant. The interactive effects of these two variables were also highly significant.' Source of Variation Degrees of Freedom Sum of Squares Mean Square "F" Values Treatments Drop Diameter Replications Treatment Error Sub-Treatment Water Layers Water Layers x Diameter Sub-Treatment Error () () () ( ) Statistical significance at the 0.01 level. Figure 3 shows that, for each 100 drops, the soil loss increased as larger waterdrops were used. When the soil samples were submerged under various depths of water, the rate of soil loss was greatest for the 5.9-, 4.7-, and 2.9-mm drops when critical water depths of, 4, and 2 mm, respectively, existed above the sample at the start of the treatment. Under deeper water layers, the amount of soil loss decreased rapidly, until no depression was apparent. EFFECT OF WATER LAYER ON SOIL LOSS THREE DROP DIAMETERS r-soil LOSS FOR KX> DROPS, jromj- WATEH LAYER, m Fig. 3 Table 1 shows the relationship of area and depth of the depression formed when water layers of various depths existed at the start of treatment. These data also indicate the variability in the depth of the water layer during the test. As the depression 14

7 deepens it fills with water, increasing the depth of water above the bottom of the depression. This greater depth of water rapidly exceeds the critical depth. As the depth of the water layer increases, the depression broadens, and the depth of the hole is lessened. TABLE 1 Relationship of area and depth of depression formed by 100 waterdrops of three selected sizes falling normally to the soil surface Depth of Water Layer, mm. Depression Average Nominal Drop Diameter, mm None () No depression formed. DISCUSSION Under the laboratory conditions described, the maximum strain for a single drop and the maximum soil loss caused by 100 drops of a similar size occurred when a critical depth of water layer was over the reference plane at the start of the treatment. These values of critical depth were determined to the nearest 2-mm increment of water layer. 147

8 As the depression formed by waterdrops striking the same point on a soil surface deepens, the depth of water layer increases, reducing the waterdrop impact force.. CONCLUSIONS By analogy, this investigation reveals several factors that probably operate under natural conditions. It may be assumed that raindrops striking a sufficiently deep water layer will decelerate, and their energy will be translated into splash and wave action. On the other hand, raindrops will readily penetrate a sufficiently shallow water layer to strike the soil surface. Under certain conditions, a raindrop may increase its mass by some added virtual mass, because of the presence of a water layer. The resultant impact forces will then be greater than if the soil surface were bare. ACKNOWLEDGMKNT Edwin A. Harre, Concervation Engineering Technician, offered helpful suggestions and carried out the procedures reported on in this paper. REFERENCES C 1 ) PALMER, R. S., An Apparatus for Forming Waterdrops. USDA, ARS, Production Research Report, No 3, Washington, 192. ( 2 ) PERRY, C.C., and H.R. LISSNER, The Strain.Gage Primer. McGraw-Hill Book Company, Inc., New York, ( 3 ) RICHARDSON, E.G., Dynamics of Real Fluids, Edward Arnold, Ltd., London,