Basic rainwater collection calculations: Difference between revisions

Latest revision as of 21:55, 15 January 2024

This page describes some basic math for calculating the potential collection of a rainwater harvesting system.

Collection calculations[edit | edit source]

$V=R\times A\times k\times e$

Where:

Symbol	Description	Units	Notes
V	Volume of collection	gal/time or m³/time	Use this to help determine tank size
R	Precipitation	inches/time or mm/time	Collect this data or find it from existing climate data
A	Footprint of collection surface	ft² or m²	This is horizontal projected area of the collection surface. For a rectangular house, use length times width.
e	Efficiency of collection surface	unitless	.75 soil,.8 average,.95 metal^[1]
K	Conversion	7.48 gal/ft³ or SI	You can also combine the 1ft/12in conversion for the precipitation data here.

US example[edit | edit source]

Rainfall for Columbia, graphed from NOAA and ggweather.

A 1900 square foot house with slanted shingle roof in Columbia, Missouri can collect a potential 2500 gallons in the month of March:

$V=R\times A\times k\times e$

March\ total\ volume={\frac {2.64in}{mo}}\times {\frac {1ft}{12in}}\times 1900ft^{2}\times {\frac {7.48gal}{ft^{3}}}\times 0.8

March total volume = 2500 gallons for the month

SI example[edit | edit source]

A 100 square meter house with concrete roof in Santo Domingo, Dominican Republic can collect a potential 13,050 liters (3,447 gallons) in the month of July:

$V=R\times A\times k\times e$

July total volume = 13,050 liters for the month

Spreadsheet calculator[edit | edit source]

Here is a link to a spreadsheet that takes into consideration the size of tank and the use of the water. The spreadsheet accepts as input the precipitation, collection area, efficiency of the roofing material and the use in order to output the collection amounts and warnings if the need outweighs the availability for a month or if the availability is declining over time.

Online calculator[edit | edit source]

A Rainwater Collection Calculator assists in designing a rainwater catchment system. Instructions on how to use the tool as well as the basis for all calculations are presented at Rainwater Collection Calculator.

Another useful calculator is the rainwater collection calculator from Good Calculators, which allows you to estimate the rainwater harvesting potential within a calendar year based on monthly historical rainfall data. This rainfall collection calculator uses the National Climatic Data Center's (NCDC) 30-year average rainfall data for the area of interest.

Tips[edit | edit source]

Keep in mind that this can be calculated per year, month, day, etc. Errors result from low time resolutions because the tank will be filling from rain and emptying from use midcycle. High time resolutions are hard to come by and require more calculations.
For a quick figure you can use the rule of thumb of 0.5 gallons per square foot per inch of rain.^[2]
For an even quicker figure you can use SI units with this calculation: The roof efficiency (e.g. 0.8) in liters per m² of roof (equivalent to 0.8 mm of rain).^[3]

Next steps[edit | edit source]

The spreadsheet could be developed to:
- make best guesses at best tank size
- calculate the buyback time depending on cost of the system and cost of water
This should have the easier metric example as well
More links for worldwide precipitation data
Table of rainwater collection efficiency coefficients for various roofing material.
A page that builds up the basics with simple drawings.

Pipe sizing calculations[edit | edit source]

Too small of pipes will restrict water from flowing through the system fast enough.

Rule of thumb: 1cm² of gutter cross section per 1m² of roof area.^[4]

Another method would be to use pipe sizing/friction tables to find an acceptable amount of friction.

Example[edit | edit source]

Using rule of thumb: for a 23m² the minimum pipe size is 23 cm².

Converting to diameter from the equation of $Area=\Pi \times \left({\frac {Diameter}{2}}\right)^{2}$ $Area=\Pi \times \left({\frac {Diameter}{2}}\right)^{2}$ , yields:
- $Diameter=2\times {\sqrt {\frac {Area}{\Pi }}}$
- $2\times {\sqrt {\frac {23cm^{2}}{\pi }}}=5.41cm$
Converting to inches, yields:
- $5.41cm\times {\frac {1in}{2.54cm}}=2.13in$

Therefore a pipe diameter of at least 2.13 inches should be used. The most common size that meets that requirement is 2.5 inch.

First flush calculations[edit | edit source]

Because of contamination on the roof the first volume of rain should be diverted from the storage tank. As a rule-of-thumb, contamination is halved for each mm of rainfall flushed away.^[5]

Calculation: meters squared (roof area) X pollution factor^[5]= liters to be diverted.

or

Time based rule-of-thumb: Divert the first 10 minutes of rain. Downpour rain per minute * 10 minutes = volume to divert

or

Area based rule-of-thumb: 0.41 liters for every meter squared of roof^{[verification needed]} OR 10 gals for every 1,000 foot squared of roof^[6]

Below is a link to a first flush volume and length calculator based on last rule of thumb

https://docs.google.com/spreadsheets/d/e/2PACX-1vRtO8QKZ55vUJ6-RqEXiOysiCxIrbn5MnEdMTWJSv1EerLO9rx_XjOWXyV-CrXHw81VggKmjYh7Mvpn/pubhtml

External links[edit | edit source]

Global precipitation data from NOAA

References[edit | edit source]

↑ Tim Dower at Rooftop efficiencies
↑ This.5 gal per square foot per inch of rain assumes about 0.8 roof efficiency, as 1 in * 1 ft/12 in * 1 ft² * 7.48 gal/ft³ * 0.8 =.499 gal.
↑ This <roof efficiency value> describes the liters per square meter [L/m²] and is equivalent to [mm]. If 1 liter would be given into a glas box with an area of 1m x 1m (1 L/m²), the water depth would be 1mm. SI units are great! 1 mm * 1/1000 m/mm * 1 m² * 1000 l/m³ * 0.8 =.8 liters. Notice how the m to mm conversion cancels with the l to m3 conversion.
↑ Rainwater Catchment for Domestic Supply. Gould, John and Niessen-Petersen, Erik. ITDG Publishing 2003. Page 75.
↑ ^5.0 ^5.1 http://web.archive.org/web/20101125005317/http://eprints.libr.port.ac.uk:80/archive/00000083/
↑ "One rule of thumb for first-flush diversion is to divert a minimum of 10 gallons for every 1,000 square feet of collection surface. However, first-flush volumes vary with the amount of dust on the roof surface, which is a function of the number of dry days, the amount and type of debris, tree overhang, and season." Excerpt from the Texas Manual on Rainwater Harvesting, 2005, pg 8.

Page data
Authors	Lonny Grafman
License	CC-BY-SA-3.0
Language	English (en)
Translations	Turkish, Chinese, Vietnamese, Indonesian, Hindi
Related	5 subpages, 30 pages link here
Impact	34,082 page views
Created	March 17, 2009 by Lonny Grafman
Modified	January 15, 2024 by 2A02:8388:4C1:7980:B814:6EF4:C057:D205
Cite as	Lonny Grafman (2009–2024). "Basic rainwater collection calculations". Appropedia. Retrieved April 26, 2024.
API queries	basic, semantic, html, files, more

[1] Tim Dower at Rooftop efficiencies

[2] This.5 gal per square foot per inch of rain assumes about 0.8 roof efficiency, as 1 in * 1 ft/12 in * 1 ft² * 7.48 gal/ft³ * 0.8 =.499 gal.

[3] This <roof efficiency value> describes the liters per square meter [L/m²] and is equivalent to [mm]. If 1 liter would be given into a glas box with an area of 1m x 1m (1 L/m²), the water depth would be 1mm. SI units are great! 1 mm * 1/1000 m/mm * 1 m² * 1000 l/m³ * 0.8 =.8 liters. Notice how the m to mm conversion cancels with the l to m3 conversion.

[4] Rainwater Catchment for Domestic Supply. Gould, John and Niessen-Petersen, Erik. ITDG Publishing 2003. Page 75.

[firstflush-5] 5.0 ^5.1 http://web.archive.org/web/20101125005317/http://eprints.libr.port.ac.uk:80/archive/00000083/

[6] "One rule of thumb for first-flush diversion is to divert a minimum of 10 gallons for every 1,000 square feet of collection surface. However, first-flush volumes vary with the amount of dust on the roof surface, which is a function of the number of dry days, the amount and type of debris, tree overhang, and season." Excerpt from the Texas Manual on Rainwater Harvesting, 2005, pg 8.

[1]

[2]

[3]

[4]

[5]

[6]

@@ Line 1: / Line 1: @@
-This page describes some basic math for calculating the potential collection of a [[rainwater]] catchment system.
+{{Topic notice}}
+{{Rainbook}}
+This page describes some basic math for calculating the potential collection of a [[rainwater harvesting]] system.
+== Collection calculations ==
-== Collection Calculations==
 <big><math>V=R \times A \times k \times e</math></big>
-:Where:
+Where:
 {| class="wikitable"
-|-
+! Symbol
-!Symbol
+! Description
-!Description
+! Units
-!Units
+! Notes
-!Notes
 |-
 | V
 | Volume of collection
-| gal/time
+| gal/time or m<sup>3</sup>/time
 | Use this to help determine tank size
 |-
 | R
 | Precipitation
-| inches/time
+| inches/time or mm/time
-| Collect this data or find it at [[#Precipitation Data]]
+| Collect this data or find it from [[#Precipitation Data|existing climate data]]
 |-
 | A
 | Footprint of collection surface
-| ft<sup>2</sup>
+| ft<sup>2</sup> or m<sup>2</sup>
-| This is horizontal projected area of the collection surface.  For a rectangular house, use length times width.
+| This is horizontal projected area of the collection surface. For a rectangular house, use length times width.
 |-
 | e
 | Efficiency of collection surface
 | unitless
-| .75 soil, .8 average, .95 metal <ref>Tim Dower at [http://www.harvesth2o.com/Capture_System.shtml Rooftop efficiencies]</ref>
+| .75 soil,.8 average,.95 metal<ref>Tim Dower at [http://web.archive.org/web/20161016104120/http://harvesth2o.com:80/Capture_System.shtml Rooftop efficiencies]</ref>
 |-
 | K
-| Conversion from ft<sup>3</sup> to gal
+| Conversion
-| 7.48 gal/ft<sup>3</sup>
+| 7.48 gal/ft<sup>3</sup> or SI
 | You can also combine the 1ft/12in conversion for the precipitation data here.
 |}
-=== US Example ===
+=== US example ===
-[[Image:Columbiarainfall.jpg|thumb|right|Rainfall for columbia|graphed from [http://lwf.ncdc.noaa.gov/oa/climate/normals/usnormalsprods.html NOAA] and [http://ggweather.com/normals/MO.htm ggweather]]]
+[[File:Columbiarainfall.jpg|thumb|Rainfall for Columbia, graphed from [http://web.archive.org/web/20120224035759/http://lwf.ncdc.noaa.gov/oa/climate/normals/usnormalsprods.html NOAA] and [http://ggweather.com/normals/MO.htm ggweather].]]
 A 1900 square foot house with slanted shingle roof in Columbia, Missouri can collect a potential 2500 gallons in the month of March:
-*<math> V=R \times A \times k \times e</math>
+* <math> V=R \times A \times k \times e</math>
-*<math> March\ total\ volume = \frac{2.64 in}{mo} \times \frac{1ft}{12in} \times 1900 ft^2 \times \frac{7.48 gal}{ft^3} \times 0.8</math>
-*March total volume = '''2500 gallons''' for the month
-=== SI Example ===
+<center><math> March\ total\ volume = \frac{2.64 in}{mo} \times \frac{1ft}{12in} \times 1900 ft^2 \times \frac{7.48 gal}{ft^3} \times 0.8</math></center>
-A 1000 square meter house with concrete roof in Santo Domingo, Dominican Republic can collect a potential 13,050 liters (3,447 gallons) in the month of July:
-*<math> V=R \times A \times k \times e</math>
+* March total volume = '''2500 gallons''' for the month
-*<math> July\ total\ volume = \frac{145mm}{mo} \times \frac{1m}{1000mm} \times 100 ft^2 \times \frac{1000liters}{m^3} \times 0.9</math>
-*July total volume = '''13,050 liters''' for the month
-=== Spreadsheet Calculator ===
+=== SI example ===
-[[Image:Rainwaterxlsexampleoutput.jpg|thumb|right|Output of the [http://spreadsheets.google.com/ccc?key=pUamlgck6T7cWIl75ontULA rainwater spreadsheet]]]
-[http://spreadsheets.google.com/ccc?key=pUamlgck6T7cWIl75ontULA Here] is a link to a spreadsheet that takes into consideration the size of tank and the use of the water.  The spreadsheet accepts as input the precipitation, collection area, efficiency of the roofing material and the use in order to output the collection amounts and warnings if the need outweighs the availability for a month or if the availability is declining over time.
+A 100 square meter house with concrete roof in Santo Domingo, Dominican Republic can collect a potential 13,050 liters (3,447 gallons) in the month of July:
+* <math> V=R \times A \times k \times e</math>
+[[File:100m2 rainwater calculation in DR.gif|center]]
+* July total volume = '''13,050 liters''' for the month
+=== Spreadsheet calculator ===
+[[File:Rainwaterxlsexampleoutput.jpg|thumb|Output of the [http://spreadsheets.google.com/ccc?key=pUamlgck6T7cWIl75ontULA rainwater spreadsheet].]]
+[http://spreadsheets.google.com/ccc?key=pUamlgck6T7cWIl75ontULA Here] is a link to a spreadsheet that takes into consideration the size of tank and the use of the water. The spreadsheet accepts as input the precipitation, collection area, efficiency of the roofing material and the use in order to output the collection amounts and warnings if the need outweighs the availability for a month or if the availability is declining over time.
+=== Online calculator ===
-=== Online Calculator ===
 A [http://www.pequals.com/rain/ Rainwater Collection Calculator] assists in designing a rainwater catchment system. Instructions on how to use the tool as well as the basis for all calculations are presented at [[Rainwater Collection Calculator]].
+Another useful calculator is [https://goodcalculators.com/rainwater-collection-calculator/ the rainwater collection calculator] from Good Calculators, which allows you to estimate the rainwater harvesting potential within a calendar year based on monthly historical rainfall data. This rainfall collection calculator uses the National Climatic Data Center's (NCDC) 30-year average rainfall data for the area of interest.
 === Tips ===
-*Keep in mind that this can be calculated per year, month, day, etc.  Errors result from low time resolutions because the tank will be filling from rain and emptying from use midcycle.  High time resolutions are hard to come by and require more calculations.
-*For a quick figure you can use the rule of thumb of '''.5 gallons per square foot per inch of rain'''.<ref>This .5 gal per square foot per inch of rain assumes about 0.8 roof efficiency, as 1 in * 1 ft/12 in * 1 ft<sup>2</sup> * 7.48 gal/ft<sup>3</sup> * 0.8 = .499 gal.</ref>
-*For an even quicker figure you can use SI units with this calculation: '''The roof efficiency (e.g. .8) in liters for every mm of rain on every m<sup>2</sup> of roof. <ref>This <roof efficiency value> liters per square meter of roof per mm of rain is so simple because SI units are great! 1 mm * 1/1000 m/mm * 1 m<sup>2</sup> * 1000 l/m<sup>3</sup> * 0.8 = .8 liters.  Notice how the m to mm conversion cancels with the l to m3 conversion.</ref>
-=== Next Steps ===
+* Keep in mind that this can be calculated per year, month, day, etc. Errors result from low time resolutions because the tank will be filling from rain and emptying from use midcycle. High time resolutions are hard to come by and require more calculations.
+* For a quick figure you can use the rule of thumb of '''0.5 gallons per square foot per inch of rain'''.<ref>This.5 gal per square foot per inch of rain assumes about 0.8 roof efficiency, as 1 in * 1 ft/12 in * 1 ft<sup>2</sup> * 7.48 gal/ft<sup>3</sup> * 0.8 =.499 gal.</ref>
+* For an even quicker figure you can use SI units with this calculation: '''The roof efficiency (e.g. 0.8) in liters per m<sup>2</sup> of roof (equivalent to 0.8 mm of rain).<ref>This <roof efficiency value> describes the liters per square meter [L/m²] and is equivalent to [mm]. If 1 liter would be given into a glas box with an area of 1m x 1m (1 L/m²), the water depth would be 1mm. SI units are great! 1 mm * 1/1000 m/mm * 1 m<sup>2</sup> * 1000 l/m<sup>3</sup> * 0.8 =.8 liters. Notice how the m to mm conversion cancels with the l to m3 conversion.</ref>'''
+=== Next steps ===
 * The spreadsheet could be developed to:
 ** make best guesses at best tank size
@@ Line 73: / Line 93: @@
 * A page that builds up the basics with simple drawings.
-==Pipe sizing calculations==
+== Pipe sizing calculations ==
-Too small of pipes will restrict water from flowing through the system fast enough.
-Rule of thumb:  1cm<sup>2</sup> of gutter cross section per 1m<sup>2</sup> of roof area.<ref> Rainwater Catchment for Domestic Supply. Gould, John and Niessen-Petersen, Erik. ITDG Publishing 2003. Page 75.</ref>
+Too small of pipes will restrict water from flowing through the system fast enough.
+Rule of thumb: 1cm<sup>2</sup> of gutter cross section per 1m<sup>2</sup> of roof area.<ref>Rainwater Catchment for Domestic Supply. Gould, John and Niessen-Petersen, Erik. ITDG Publishing 2003. Page 75.</ref>
 Another method would be to use pipe sizing/friction tables to find an acceptable amount of friction.
-===Example===
+=== Example ===
+[[File:Sizingrwc.JPG|thumb|Pipe size to roof area table.]]
 Using rule of thumb: for a 23m<sup>2</sup> the minimum pipe size is 23 cm<sup>2</sup>.
-#Converting to diameter from the equation of Area=Pi*(Diameter/2)<sup>2</sup>, yields:
-#*Solving for diameter, yields Diameter=2*squareroot(Area/Pi)
-#*2*Squareroot(23 cm<sup>2</sup>/pi) = 5.41 cm
-#Converting to inches, yields:
-#*5.41cm * 1in / 2.54cm = 2.13 in
-Therefore a pipe diameter of at least 2.13 inches should be used.  The most common size that meets that requirement is 2.5 inch.
-[[Image:Sizingrwc.JPG|right|Pipe size to roof area table.]]
+# Converting to diameter from the equation of <math>Area=\Pi \times \left(\frac{Diameter}{2}\right)^2</math>, yields:
+#* <math>Diameter=2\times \sqrt{\frac{Area}{\Pi}}</math>
+#* <math>2\times \sqrt{\frac{23 cm^2}{\pi}} = 5.41 cm</math>
+# Converting to inches, yields:
+#* <math>5.41cm \times \frac{1in}{2.54cm} = 2.13 in</math>
-==First Flush Calculations==
+Therefore a pipe diameter of at least 2.13 inches should be used. The most common size that meets that requirement is 2.5 inch.
-Because of contamination on the roof the first volume of rain should be diverted from the storage tank. As a rule-of-thumb, contamination is halved for each mm of rainfall flushed away <ref name="firstflush">http://eprints.libr.port.ac.uk/archive/00000083/</ref>.
+== First flush calculations ==
+Because of contamination on the roof the first volume of rain should be diverted from the storage tank. As a rule-of-thumb, contamination is halved for each mm of rainfall flushed away.<ref name="firstflush">http://web.archive.org/web/20101125005317/http://eprints.libr.port.ac.uk:80/archive/00000083/</ref>
+:Calculation: meters squared (roof area) X pollution factor<ref name="firstflush" />= liters to be diverted.
-:Calculation: meters squared (roof area) X pollution factor<ref name="firstflush"/> = liters to be diverted.
-or
-Time based rule-of-thumb: Divert the first 10 minutes of rain.
-:Downpour rain per minute * 10 minutes = volume to divert
 or
-:Area based rule-of-thumb: 0,41 liters for every meter squared of roof{{Fact|find the numbers/references for this rule of thumb and compare to first 10 minutes rule}} OR 10 gals for ever 1,000 foot squared of roof <ref>"One rule of thumb for first-flush diversion is to divert a minimum of 10 gallons for every 1,000 square feet of collection surface. However, first-flush volumes vary with the amount of dust on the roof surface, which is a function of the number of dry days, the amount and type of debris, tree overhang, and season."  Exerpt from the Texas Manual on Rainwater Harvesting, 2005, pg 8.</ref>
+:Time based rule-of-thumb: Divert the first 10 minutes of rain. Downpour rain per minute * 10 minutes = volume to divert
+or
+:Area based rule-of-thumb: 0.41 liters for every meter squared of roof{{Fact|find the numbers/references for this rule of thumb and compare to first 10 minutes rule}} OR 10 gals for every 1,000 foot squared of roof<ref>"One rule of thumb for first-flush diversion is to divert a minimum of 10 gallons for every 1,000 square feet of collection surface. However, first-flush volumes vary with the amount of dust on the roof surface, which is a function of the number of dry days, the amount and type of debris, tree overhang, and season." Excerpt from the Texas Manual on Rainwater Harvesting, 2005, pg 8.</ref>
+'''Below is a link to a first flush volume and length calculator based on last rule of thumb'''
+https://docs.google.com/spreadsheets/d/e/2PACX-1vRtO8QKZ55vUJ6-RqEXiOysiCxIrbn5MnEdMTWJSv1EerLO9rx_XjOWXyV-CrXHw81VggKmjYh7Mvpn/pubhtml
 == External links ==
-*[http://www.ncdc.noaa.gov/Isis/stationlist?networkid=1 Global precipitation data from NOAA]
+* [https://www.ncdc.noaa.gov/isis/stationlist?networkid=1 Global precipitation data from NOAA]
 == References ==
-<references/>
+<references />
+{{Page data}}
 [[Category:Rainwater]]