Problem 34 - Technical Mathematics with Calculus

Question

Convert units on the following time rates. 777 gallons per minute to cubic meters per hour.

Step-by-Step Solution

Answer

777 gallons per minute is approximately 176.52 cubic meters per hour.

Step 1: Understand the Unit Conversion

We are converting the flow rate from gallons per minute to cubic meters per hour. We need to know that 1 gallon is equivalent to 0.00378541 cubic meters.

Step 2: Convert Gallons to Cubic Meters

Multiply the flow rate by the conversion factor from gallons to cubic meters. \[ 777 \text{ gallons/minute} \times 0.00378541 \text{ cubic meters/gallon} = 2.94199117 \text{ cubic meters/minute} \]

Step 3: Convert Minutes to Hours

Since there are 60 minutes in an hour, multiply the flow rate in cubic meters per minute by 60 to get cubic meters per hour. \[ 2.94199117 \text{ cubic meters/minute} \times 60 \text{ minutes/hour} = 176.5194702 \text{ cubic meters/hour} \]

Key Concepts

Flow Rate Conversion

Understanding flow rate conversion is essential in various fields like engineering, chemistry, and everyday tasks such as plumbing. It involves changing the measurement of the volume of fluid passing through a point per unit of time from one unit to another. In our exercise, we converted a flow rate given in gallons per minute to cubic meters per hour.

To begin the conversion, you should know the relationship between the two units of volume you're converting. One gallon is equivalent to 0.00378541 cubic meters. Multiply the original flow rate by this conversion factor to switch from gallons to cubic meters. Doing the math gives us a new flow rate in cubic meters per minute. Next, adjust for the time unit by considering that one hour contains 60 minutes, thus scaling up the flow rate accordingly. As a result, you seamlessly transition from a flow rate in gallons per minute to cubic meters per hour.

Gallons to Cubic Meters

The conversion from gallons to cubic meters is a critical part of volume conversion in the metric system. Since gallons and cubic meters measure volume but use different scales, a conversion factor is necessary to translate one to the other. The conversion factor, 0.00378541, represents how many cubic meters are in one gallon.

To convert gallons to cubic meters, you multiply the number of gallons by this factor. The use of this precise conversion factor ensures accuracy, which is especially important in applications like billing for water usage, calibrating irrigation systems, or specifying tank volumes in industrial settings. It's also a useful conversion for international trade, where products might be measured in gallons in one country and cubic meters in another.

Time Unit Conversion

Time unit conversion is a process used to convert a quantity of time from one unit to another, like minutes to hours, seconds to minutes, or hours to days.

In the context of our exercise, converting flow rate from minutes to hours requires an understanding of how these time units relate. There are 60 minutes in one hour, so to convert a quantity from minutes to hours, you'd multiply by 60 if you're going from minutes to hours, or divide by 60 when going the other way. Remember that accurate time conversion is especially important in processes where timing can affect outcomes, such as cooking, scheduling, or any kind of rate-based measurements. For instance, knowing the exact flow rate of a liquid in an industrial process could be critical, and converting time units correctly will ensure the proper functioning of the process.