Formulae Related to Ponding:
Discharge
- Source of formula: "Engineering Handbook of Conversion Factors" by CE NATCO, page 142
- This formula provides a quick and surprisingly accurate method of determining the
number of Gallons Per Minute (GPM) being discharged from an open-ended horizontal pipe.
- Measure any convenient horizontal distance out from the open end of the pipe.
This distance in inches will be called "X".
- Now measure down (vertically) from the end of the "X" location to a point just
touching the flowing liquid. This distance in inches will be called "Y".
- Determine the diameter of the pipe; this will be called "d".
- GPM = (2.56 * X * d * d) / sqrt(Y)
where "X" = horizontal distance measured in inches
where "Y" = vertical distance measured in inches
where "d" = diameter of pipe in inches
- Example:
Assume the "X" = 24 inches, "Y" = 25 inches, and "d" = 2 inches
Substituting these values gives you:
GPM = (2.56 * 24 * 2 * 2) / sqrt(25)
GPM = (2.56 * 96) / 5
GPM = 49.15 gallons per minute
GPH = 49.15 * 60 = 2949 gallons per hour
- This formula generates values which are slightly smaller than those found in
the table for "Horizontal Pipe Discharge".
- Source of formula: "Pocket Ref" by Thomas J. Glover, page 419
- The following table contains information about the column of
water which exits a
horizontal pipe.
- Units are in inches
- Discharge length = length of horizontal water column BEFORE the
water curves
downward 4 inches due to gravity
- Water flow (in GPH) in pipes of various diameters
- Here are some sample discharge lengths:
Horizontal
Discharge
in Inches | GPH for
1-inch
Pipe | GPH for
1.5-inch Pipe | GPH for
2-inch
Pipe | GPH for
2.5-inch Pipe | GPH for
3-inch
Pipe | GPH for
4-inch Pipe |
| 4 | 360 | 780 | 1320 | 1860 | 2880 | 4980 |
| 5 | 420 | 1020 | 1620 | 2340 | 3660 | 6240 |
| 6 | 480 | 1200 | 1980 | 2820 | 4380 | 7500 |
| 7 | 600 | 1380 | 2280 | 3300 | 5100 | 8760 |
| 8 | 660 | 1560 | 2640 | 3720 | 5820 | 9960 |
| 9 | 780 | 1800 | 2940 | 4200 | 6600 | 11220 |
| 10 | 840 | 1980 | 3300 | 4680 | 7320 | 12480 |
| 11 | 960 | 2160 | 3600 | 5160 | 8040 | 13740 |
| 12 | 1020 | 2400 | 3960 | 5640 | 8760 | 15000 |
- Source of formula: "Pocket Ref" by Thomas J. Glover, page 421
- The following formula is an approximation of the output of a
vertical pipe:
GPM = sqrt(H) * K * D * D * 5.68
where
GPM = gallons per minute,
H = height of water above the end of the pipe, in inches
D = diameter of pipe in inches
K is a pipe constant which ranges from 0.87 to 0.97.
- This formula could be rearranged as follows:
H = (GPM / (K * D * D * 5.68))**2
- Here are some sample calculations for vertical pipes using K equal
to 0.87:
| GPH | GPM | Water Height
for 1-inch
Pipe | Water Height
for 1.5-inch Pipe | Water
Height
for 2-inch Pipe | Water height
for 3-inch
Pipe |
| 60 | 1 | 0.0409
" | 0.0081 " | 0.0026 " | 0.0005 " |
| 300 | 5 | 1.0238
" | 0.2022 " | 0.0640 " | 0.0126 " |
| 600 | 10 | 4.0950
" | 0.8089 " | 0.2559 " | 0.0505 " |
| 900 | 15 | 9.2314
" | 1.8200 " | 0.5758 " | 0.1137 " |
| 1200 | 20 | 16.3793 " | 3.2356 " | 1.0238 " | 0.2022 " |
| 1500 | 25 | 25.5939 " | 5.0557 " | 1.5996 " | 0.3160 " |
| 1800 | 30 | 36.8558 " | 7.2802 " | 2.3034 " | 0.4550 " |
| 2100 | 35 | 50.1648 " | 9.9091 " | 3.1352 " | 0.6193 " |
| 2400 | 40 | 65.5213 " | 12.9425 " | 4.0950 " | 0.8088 " |
| 2700 | 45 | 82.9253 " | 16.3804 " | 5.1829 " | 1.0238 " |
| 3000 | 50 | 102.3757 " | 20.2227 " | 6.3985 " | 1.2639 " |
- At the same GPH, the water column of a one-inch pipe is 16 times
higher than the
water column of a two-inch pipe!
- Doubling the flow rate will generate a water column four times
higher in the same
pipe.
- Sources of the formula: mort@mauimail.com and "Pocket Ref" by Thomas J. Glover, page
421
- Characteristics of the Francis Formula
- Works best in calm waters
- Formula overestimates the flow for very small weirs
- Best accuracy is for weirs 5-10 feet wide and 1 foot high
- Weir is in the center of the stream
- At least 3 times the weir's height from each end of the weir to the
bank
- Formula is an APPROXIMATION of the actual volume flowing over
the waterfall
- Francis Formula for a waterfall:
Flow = 3.33 * ( ( W - 0.2 * H ) * H ^ 1.5 ) in CFS
where
W = width of weir in feet
H = height of water flowing through weir in feet
CFS = cubic feet per second
- Sample calculation:
H = 1/2 inch = 0.04167 feet
W = 6 inches = 0.500 feet
Flow = 3.33 * ( ( 0.500 - 0.2 * 0.04167 ) * 0.04167 ^ 1.5
Flow = 3.33 * ( ( 0.500 - 0.008334 ) * 0.0085
Flow = 3.33 * ( ( 0.491666 ) * 0.0085
Flow = 0.013917 cubic feet per second
Flow = 0.013917 cf/s * (3600 sec/hour)
Flow = 50.099 cf/hr
Flow = 50.099 cf/hr * ( 7.48052 g/cf )
Flow = 374.77 GPH
- Here are some sample calculations (overestimations) for several
small weirs:
Water
Height
(Inches) |
GPH for
3-inch
Weir | GPH for
6-inch
Weir |
GPH for
9-inch
Weir | GPH for
12-inch
Weir |
GPH for
18-inch
Weir | GPH for
24-inch
Weir |
GPH for
36-inch
Weir |
| 0.25 |
66 | 134 | 201 |
268 | 403 | 538 |
808 |
| 0.50 |
184 | 375 | 566 |
756 | 1137 | 1518 |
2280 |
| 0.75 |
333 | 683 | 1033 |
1384 | 2084 | 2785 |
4186 |
| 1.00 |
503 | 1043 | 1582 |
2121 | 3200 | 4278 |
6436 |
| 1.25 |
691 | 1445 | 2198 |
2952 | 4460 | 5967 |
8982 |
- Rules of thumb
- 100 GPH will produce a stream 1/2 inch deep and 1 inch wide.
- 325 GPH will produce a steam 1/2 inch deep and 6 inches wide;
the formula yields a value of 375 GPH.
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bonniehill@verizon.net
last modified on January 19, 2006
URL:
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Estimating Liquid Discharge from Pipe