The constant 5940 in the formula for calculating Gallons Per Minute (GPM) is derived from the conversion factors needed to calculate the rate of liquid application in agricultural spraying. Here’s a detailed breakdown of its significance:
GPM = Gallons per acre ×Speed (mph)×Nozzle Spacing (inches) / 5940
To understand the 5940 constant, let’s look at the units involved and how they are converted:
- Gallons Per Acre (GPA): This is the desired rate of application in gallons per acre.
- Speed (mph): This is the speed at which the sprayer travels, measured in miles per hour.
- Nozzle Spacing (inches): This is the distance between the nozzles on the sprayer boom, measured in inches.
To convert these measurements into a flow rate (GPM), we need to account for the following conversions:
- Acres to square feet: 1 acre = 43,560 square feet
- Miles to feet: 1 mile = 5,280 feet
- Inches to feet: 1 foot = 12 inches
Breaking Down 5940 Constant in GPM Formula
1. Convert Speed (mph) to feet per minute (fpm):
Speed in mph needs to be converted to fpm because we need a flow rate per minute.
Since 1 mile = 5,280 feet and 1 hour = 60 minutes:
Speed (fpm) = Speed (mph) × 5280 feet/60 minutes = Speed (mph) × 88 feet per minute
2. Convert Nozzle Spacing (inches) to feet:
Nozzle Spacing in inches needs to be converted to feet.
Nozzle Spacing (feet) = Nozzle Spacing (inches)/12
3. Calculate the area covered per minute (square feet per minute):
The area covered per minute by a sprayer is the product of the speed in feet per minute and the nozzle spacing in feet.
Area (square feet per minute) = Speed (fpm) * Nozzle Spacing (feet) = (Speed (mph) * 88) * (Nozzle Spacing (inches) / 12)
4. Convert Area (square feet per minute) to acres per minute
1 acre = 43,560 square feet, so:
Acres per minute = Area (square feet per minute) / 43,560 = ((Speed (mph) * 88) * (Nozzle Spacing (inches) / 12)) / 43,560
5. Combine conversions into one formula
Simplifying the expression by combining constants:
GPM = GPA * Acres per minute
= GPA * (((Speed (mph) * 88) * (Nozzle Spacing (inches) / 12)) / 43,560)
= GPA * (Speed (mph) * Nozzle Spacing (inches) * 88) / (43,560 * 12)
= GPA * (Speed (mph) * Nozzle Spacing (inches) * 88) / 522,720
Simplifying the constant:
522,720 divided by 88 gives us 5940. GPM = (GPA * Speed (mph) * Nozzle Spacing (inches)) / 5940
Therefore, the constant 5940 is a result of combining the necessary unit conversions to calculate the flow rate in gallons per minute based on the application rate in gallons per acre, the speed of the sprayer in miles per hour, and the nozzle spacing in inches.