Question

A well has an hour meter attached to a water meter totalizer. After 3 hours of operation, the well produced 279,000 gallons. Water is the well yield in gpm?

Short answer

1,550 gpm

Step-by-step solution

- Understand the Problem

The problem is asking for the yield of the well in gallons per minute (gpm). We know the well produced 279,000 gallons in 3 hours.

- Convert Hours to Minutes

Since we need the yield in gallons per minute, we first convert the time from hours to minutes. There are 60 minutes in an hour, so we multiply the number of hours by 60:\[3 \text{ hours} \times 60 \text{ minutes/hour} = 180 \text{ minutes} \]

- Calculate the Yield in Gallons Per Minute

To find the yield in gpm, we divide the total gallons produced by the total number of minutes:\[\frac{279,000 \text{ gallons}}{180 \text{ minutes}} \]

- Perform the Division

Perform the division to find the yield:\[\frac{279,000}{180} = 1,550 \text{ gpm} \]

Key concepts

gallons per minute (GPM)

Understanding how to calculate gallons per minute (gpm) is important for determining the efficiency of water-supply systems like wells. In this exercise, we are given that a well produced 279,000 gallons of water in a 3-hour period. Our aim is to convert this amount into a rate that tells us how many gallons are produced each minute. The formula for calculating gpm is simple: you divide the total gallons produced by the total time in minutes. This allows you to evaluate how much water is generated consistently over time, which is very useful for various applications like irrigation, industrial processes, and drinking water supplies.

Remember, gallons per minute is a flow rate. It’s a measurement of the volume of water flowing past a point in a given time frame. This is different from total volume, which is just the amount of water, without considering how fast or slow it moves.

water totalizer

A water totalizer is a device used to measure the cumulative amount of water that flows through a system. In our example, the well has an hour meter attached to a water meter totalizer. This setup records the total volume of water used over a certain period, allowing us to track water usage or production.

The water totalizer works by continuously recording the total amount of water that has passed through the system. This is crucial for tasks such as monitoring water resource consumption, managing utility billing, or determining the efficiency of a water supply system.

Using the data from the water totalizer (279,000 gallons in this case), we can carry out further calculations to find rates like gallons per minute, or analyze the performance of the system over varying time intervals.

conversion of units

Converting units is a fundamental skill in science and engineering. In the original exercise, we need to convert hours to minutes because the problem asks for yield in gallons per minute (gpm). There are 60 minutes in an hour, so to convert the total operation time from hours to minutes, you multiply by 60.

For instance, if the well operated for 3 hours, you convert this to minutes by calculating:

• 3 hours × 60 minutes/hour = 180 minutes

Unit conversion ensures that you're working with comparable units in your calculations. This is particularly vital in cases involving rates of change, like flow rates in gpm. Careful attention to unit conversion from hours to minutes, or other necessary conversions, is essential for accurate results.

In summary, unit conversion is a straightforward, yet essential process that enables proper calculation and comprehension of scientific and mathematical problems.