Complete in Metric Conversions:
A lawn sprinkler covers a rectangular pattern of 20ft x 30ft. if the flow rate of the sprinkler is 2.5 gpm, derive a formula for calculating the time (hours) to apply D inches of water over one 20ft x 30ft area. What are the units on the constant?
To derive the formula, we need to convert the given values to a consistent set of units.
First, let's convert the measurements of the rectangular area from feet to square inches:
20ft x 30ft = 600 square feet
1 square foot = 144 square inches (since 1ft = 12in)
So, the area in square inches is 600 x 144 = 86,400 square inches.
Next, let's convert the flow rate from gallons per minute (gpm) to cubic inches per minute:
1 gallon = 231 cubic inches
2.5 gpm = 2.5 x 231 = 577.5 cubic inches per minute.
Now, we need to calculate the time (in minutes) it takes to apply D inches of water over the given area. We can use the formula: time = (area * depth) / flow rate.
Substituting the values, the formula becomes:
time (in minutes) = (86,400 square inches * D inches) / 577.5 cubic inches per minute.
To convert the time from minutes to hours, we divide it by 60 since there are 60 minutes in an hour:
time (in hours) = (86,400 square inches * D inches) / (577.5 cubic inches per minute * 60 minutes per hour).
Now, simplifying the formula further:
time (in hours) = (86,400 * D) / (577.5 * 60) = D / 3.8.
Therefore, the formula for calculating the time (hours) to apply D inches of water over one 20ft x 30ft area is D / 3.8. The units on the constant 3.8 are "inches per minute."