A lawn sprinkler covers a rectangular pattern of 20ft x 30ft.
1)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.
2)What are the units on the constant?
To derive a formula for calculating the time to apply a certain amount of water over a given area, we need to consider the flow rate of the sprinkler and the dimensions of the area being covered.
1) Let's start by finding the volume of water needed to cover a 20ft x 30ft area with a certain depth D. The volume can be calculated by multiplying the area by the depth:
Volume = Area x Depth
Volume = (20ft x 30ft) x D
Next, we need to convert the volume from cubic feet to gallons. Since 1 cubic foot is approximately equal to 7.48 gallons, we can multiply the volume by 7.48 to convert it to gallons:
Volume (in gallons) = Volume (in cubic feet) x 7.48
Volume (in gallons) = (20ft x 30ft x D) x 7.48
Now, we can calculate the time required to apply this amount of water considering the flow rate of the sprinkler. The time can be calculated by dividing the volume by the flow rate:
Time (in hours) = Volume (in gallons) / Flow rate (in gpm)
Let's substitute the calculated volume and given flow rate into the formula:
Time (in hours) = [(20ft x 30ft x D) x 7.48] / 2.5
Therefore, the formula to calculate the time (in hours) to apply D inches of water over a rectangular area of 20ft x 30ft using a sprinkler with a flow rate of 2.5 gpm is:
Time (in hours) = [(20ft x 30ft x D) x 7.48] / 2.5
2) The constant in the formula is the conversion factor for converting cubic feet to gallons, which is 7.48. The units on this constant are gallons per cubic foot (gallons/ft³) since it is used to convert the volume from cubic feet to gallons.