 Physical Science - Other

# How to Convert Gpm to Velocity Stephen Bredenkamp's image for:
"How to Convert Gpm to Velocity"
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Image by: A gallon is three dimensional, a measure of volume, similar to cubic feet. In fact, 1 US gallon is equal to 231 cubic inches, or 0.133680 cubic feet. Alternatively 1 cubic foot equals 7.48 gallons. This article refers to the US Customary gallon: it differs from the UK Imperial gallon of 277.42 cubic inches.  (Reference: Online dictionary: http://dictionary.reference.com/browse/gallon

Velocity is one dimensional and represents the speed of an object. Comparing water flowing down the Mississippi River to water flowing through a water pipe, it is immediately evident that the relationship between GPM and velocity has to depend on the cross section of the flow. The Mississippi River, at one point half a mile (2640 feet) wide and 40 feet deep will have a flow of millions or even tens of millions of gallons per minute, even at a relatively low speed. However a water pipe with a diameter of ½ inch has a relatively low GPM, even when the water seems to squirts out.

The conversion from GPM to feet per minute (velocity) requires a conversion from gallons to cubic feet (using the factor of 0.133680 as defined above). As this amount of water in cubic feet has to flow through the pipe (or river) with the known cross-section in a minute, the calculation divides the cross-section (two dimensional) into the volume (three dimensional) to calculate the length of pipe required to hold that amount of water. So the formula will be

Speed (feet per minute) = GPM*0.133680/cross-section (square feet).

As an example, assume the water pipe is ½ inch (1/24 feet) in diameter. The cross section will then be (pi * radius * radius) = 0.005454 square feet. A gallon is 0.133680 cubic feet, so the pipe needs to be (0.133680/0.005454) = 24 feet long to hold a gallon. The speed is therefore 24 feet per minute, about 0.5 feet per second.

The Mississippi, however, at one point is 2640 feet wide and 40 feet deep, so it has a cross section of 105600 (2640*40) square feet. One gallon, or 0.133680 cubic feet would only need a length of 0.133680/105600 feet, which equals 0.0000013 feet, giving a speed of 0.0000013 feet per minute.

The floods in April 2011 had an estimated peak flow of 2 million cubic feet per second, which is equal to (2,000,000*60*7.48 GPM) or 900 million GPM. 900 million GPM will equate to (900,000,000*0.133680/105600) feet per minute, a speed of 1139 feet per minute.  (References listed below)

Consider a wall of water, half a mile wide, 40 feet high, coming towards you at over 1000 feet per minute, and you start to feel the immense power of a river in flood!

References: There are various references for the depth and flow of the Mississipi during the recent floods. This article refers to a depth of 40 feet for ease of calculation. According to ABC News it crested at 47 feet. An article in Wikipedia refers to a flow of 2,340,000 cubic feet per second, which has been rounded down to 2,000,000 cfs for ease of calculation.

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• http://dictionary.reference.com/browse/gallon
• http://abcnews.go.com/US/mississippi-flooding-river-cresting-louisiana-prepares-rising-waters/story?id=13567600
• http://en.wikipedia.org/wiki/2011_Mississippi_River_floods