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.
2)What are the units on the constant?
To calculate the time (in hours) to apply a certain amount of water (in inches) over a 20ft x 30ft area, we need to consider the flow rate of the sprinkler.
First, let's convert the dimensions of the area from feet to square inches by multiplying by 12 (since there are 12 inches in a foot):
Area = 20ft x 30ft = (20ft x 12in/ft) x (30ft x 12in/ft) = 240in x 360in = 86,400 square inches
Now, let's derive the formula for calculating the time (in hours) to apply D inches of water:
Time = (Area * D) / Flow rate
Substituting the values we have:
Time = (86,400 square inches * D inches) / 2.5 gpm
Notice that the flow rate is in gallons per minute (gpm). To convert this into the appropriate units for time, we need to take into account that there are 128 fluid ounces in a gallon and 60 minutes in an hour.
Converting the flow rate from gpm to square inches per hour:
Flow rate = 2.5 gpm * (128 fluid oz/gallon) * (1 gallon / 60 mins) * (60 mins / 1 hour)
Flow rate = 2.5 * 128 / 60 square inches per hour
Therefore, the formula for calculating the time (in hours) to apply D inches of water is:
Time = (86,400 square inches * D inches) / [(2.5 * 128 / 60) square inches per hour]
Now, let's move on to the second question:
The units on the constant in the formula are "square inches per hour". This means it is the rate at which water is being applied over an area, specifically how many square inches are covered with water in one hour.