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Home//Municipal//Engineering Tools & Calculators//Modified Manning Calculators//Program Methodology
Program Methodology
Test Program to Determine Inlet Grate Capacities for Gutter Flow
The effort to provide roadway drainage structures which would assure safe travel for bicycle riders prompted a review of drainage inlet grates directed toward determining a proper design. Those involved in the sale and manufacture of these products at Neenah Foundry were also aware that very little information was available concerning the actual flow capacity of the large variety of grates in production by the company.
Engineering Laboratory Design, Inc. was retained to design and build the necessary test equipment to determine and evaluate the hydraulic characteristics of inlet grates. These facilities were completed in the spring of 1974 and installed in an enclosed area of the pattern storage building located at Plant 2 in Neenah, Wisconsin. Engineering Laboratory Design, Inc. was retained as consultant for the development and implementation of the testing program.
Test Facilities
On consideration of the factors involved in obtaining useful information which would be of value to those engaged in design work, it was concluded that a program of testing or calibrating full size units would be the most desirable. Test studies could have been successfully carried out with hydraulic models but this would have required that scaled-down grates be used. Such models would have been more costly than using the prototype castings and would have probably meant delays in the test program. In addition, the test information may be been questioned by those not familiar with model study procedures.
To permit full scale testing, a hydraulic flume (channel) of overall length of 25 feet and four feet wide was constructed. This unit is comprised of a 19-foot length of Plexiglas viewing channel with a three-foot inlet section to provide proper uniform flow conditions. The grate under test is placed in the floor of the downstream end of the channel. Flow passing through the grate is returned to the reservoir below the flume while the flow by-passing the grate is measured by a sharp-crested straight weir before returning to the reservoir. The difference between the gutter flow and the by-pass quantity is the capacity of the grate under test. To simulate a wide range of flow conditions the flume is so constructed that it can be tilted both in a longitudinal and transverse direction. This is accomplished by a system of hydraulic cylinders. A maximum slope of 10% in either direction can be obtained.
In order that the surface of the flume would simulate a roughness found in brushed concrete or black top finish, the flow of the flume was lined with a chip surface roofing paper. Calculations of Manning's "n" from test data indicated that this surface has a roughness coefficient of between 0.013 and 0.014. This is close to the accepted values used by other investigators.
The channel width of four feet is thought to represent normal gutter flow conditions for most pavements and is sited as adequate by Guillou. 1
Instrumentation
Various flow parameters were obtained both by direct measurement and by several electronic devices. The inflow to the flume was obtained by a differential pressure gage connected to a sharp edged orifice in the supply line. Through a specially calibrated dial the gage reads directly in cubic feet per second. The flow was frequently checked by differential manometer also connected to the orifice. The by-pass quantity, measured by the straight weir, was read from a dial indicator operated by a float connected to the pool behind the weir.
The flow depth upstream of the grate inlet was measured by a standard point gage and also by means of a transducer with readout by a digital voltmeter.
The slope of the flume could be adjusted to any position within the range with aid of electronic angle measuring units with a resolution to within 1/10 of 1 degree. The slope was rechecked after every change in position.
Theory
The velocity of water in a natural or man-made channel is governed principally by the slope along the axis of the channel, the shape of the channel cross-section, and the roughness of the surface in contact with the water, also known as the wetted perimeter.
The most generally used formula or equation is one developed by an early hydraulic investigator by the name of Manning. This expression is familiar to all hydraulic designers and is shows in the following form:
V = (1.486/n)R2/3S1/2 where:
- V = Velocity of flow in ft./second
- n = Roughness coefficient
- R = Hydraulics radius-defined as the area/wetted perimeter
- S = Slope of the longitudinal axis of channel in ft./ft.
Where the width of the channel cross section is relatively great in respect to the depth of flow, the depth can be used as the value of R. The depth is considered to be the depth at the curb.
The discharge, Q in cubic feet per second, is obtained by multiplying the area which, for rectangular channels, is width x depth, x the velocity of flow. Thus the equation of discharge becomes Q = AV = WDV where:
V = (1.486/n)D2/3S1/2 then Q = (1.486/n)WD5/3S1/2
When the flow in the gutter takes the shape of a triangular channel the Manning equation has been modified by Izzard 2 to include the transverse slope and has the following form:
Q = (.56Z/n)D8/3S1/2 where Z is reciprocal of the cross-slope and D is the depth or head (h) in feet.
The 8/3 power of the depth arises from the flow area being a function of D2. This form of the equation describes the flow in a triangular section very accurately and computations of discharge for the test flows in the approach channel agree very closely with the actual values.
When the test data are plotted logarithmically for given longitudinal and transverse slopes a relationship between Q and D is observed which closely follows the Manning equation.
If the term (1.486/n)WS1/2 is combined to become K' this relation simplifies to Q = K'D5/3. Further consideration of the interception process indicates that the quantity that can be removed is limited to the water flowing in that portion of the gutter equal to the grate width. Minor additions to the grate flow will occur due to inflow from the side of the grate. No attempt was made to include a factor measuring side flow since this would unnecessarily complicate the equation.
The discharge through the gutter section equal to the grate width similarly has a discharge-depth relation which can be expressed by Q = KD5/3 where K is unique to the geometry of each grate. Analysis of the test data revealed that the discharge did not follow the slope term (S½) closely, therefore a general equation for each transverse slope could not be used. Consequently K values for each tested combination of longitudinal and transverse slope for a specific grate installation were evaluated.
The geometry of the inlet grate also governs the capacity of the system. Long narrow bars parallel to the direction of flow are, with one exception, the most efficient arrangement. As cross-bars are added to reduce size of openings or for strength reasons the potential capacity of the grate is reduced. Cross-bars form barriers to the smooth flow of water through the grate and will often deflect the jet upward, further interfering with the flow through the grate. For a theoretical analysis of this action see Guillou 1, Fig. 3, page 17. Thick wide bars permit a portion of the flow to reach the far end of the grate. A grate made up entirely of cross-bars whose shape is patterned after an air foil and positioned to turn the flow at an angle with the vertical is the most efficient geometry available.
Tests were run on all grates using a standard procedure. Six rates of gutter flow were run for each of four longitudinal and four different cross-slopes with a total of 96 separate test points for each complete grate test. Values of the grate constant "K" were obtained for each combination of longitudinal and cross-slope. Each test point was computed and compared with the observed value. Comparison of these values indicates that an average accuracy of individual point is about 5% with the maximum deviation being about +/-10%. Considering the number of variables involved and the accuracy with which each could be observed, the correlation is quite acceptable.
The data from the grate tests has been compiled in graph form with values of "K" plotted vs. the transverse gutter cross-slope. A series of curves showing the "K" values for each longitudinal slope allows the selection of grate coefficients for most generally used slopes. Values of "K" for slopes between those plotted can be obtained by extrapolation. Slopes less than 1% longitudinal were not tested since this would represent a condition where the pavement would be flooded.
In determining the inlet grate capacity for a specific grate, the value of "K" is chosen from the graph using the proper longitudinal and transverse slope to fit the design case. "Values of K vs ST are given for each longitudinal slope SL. These slopes are indicated in percent of slope". The "K" selected is then used in the equation Q = KD5/3 where D is the depth upstream of the grate in feet. D can be obtained from rating tables, in Federal or State Highway design manuals, for the proper slope, shape and surface roughness or can also be developed from Izzard's 2 modification of the Manning's equation if the rating tables are not available. The equation is given in the preceding part of this discussion. For convenience values of D5/3 are given for most commonly used depths.
Table of Values of D5/3
| D | D5/3 |
|---|---|
| .05 | .00680 |
| .07 | .0119 |
| .08 | .0148 |
| .09 | .0181 |
| .10 | .0215 |
| .12 | .0292 |
| .14 | .0377 |
| .16 | .0471 |
| .18 | .0573 |
| .20 | .0684 |
| .22 | .0801 |
| .24 | .0926 |
| .26 | .106 |
| .28 | .120 |
| .30 | .134 |
Spacing Selection
Gutter flow which determines inlet spacing can only be estimated from hydrologic data and with less accuracy than the information derived from the inlet capacity studies. A number of methods may be used to determine the gutter flow and from values obtained, a spacing of the inlets can be determined such that the inlet can accommodate all or the major portion of the discharge. The next interval must then be adjusted so that the flow plus the carry-over will be within acceptable limits. Examples of pavement flow calculations are found in several publications. 1, 3 Allowing some carry-over to occur will result in fewer inlets for a given length of slope; however the inlet at the base of the grade must be spaced so that the area is not flooded.
See the Determination of Inlet Spacing section for the solution to a typical inlet spacing problem.
Explanation of Charts
The values shown on the graphs which follow the explanation section of this manual, are the results of actual testing on a full size hydraulic testing flume and were not determined by computation.
Each graph has a drawing in the upper right hand corner of the page which shows the overall dimensions of the grate, the grate type and direction of flow used in testing. These sketches are representative and are not drawn to scale. For flow-through opening size refer to catalog "R".
The catalog number, description, and component computer code number are shown in the upper left-hand corner of the graph. This information can be used for ordering your casting choice.
Having Trouble?
For additional information regarding Neenah Inlet Grate Capacities, please contact Steven Akkala P.E., at (920) 729.3653 or email at steve.akkala@neenahenterprises.com.
Bibliography
- Guillou, J. C. "The Use and Efficiency of Some Gutter Inlet Grates," Univ. of Illinois Eng. Experiment Station Bulletin #450.
- Izzard, C. F. "Tentative Results on Capacity of Cub Opening Inlets," Research Report No. 11-B on Surface Drainage, Highway Research Board, Washington, D. C. 1950
- Cassidy, J. J. "Generalized Hydraulic Characteristics of Grate Inlets," Highway Research Board Record No. 123, Highway Research Board, Washington, D. C.
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