Question

A small water system has one well that pumps 250 gpm. This well serves a population of 1,575 with an average gpcd of 195 . How many hours per day must this well run to meet the demand?

Short answer

The well must run approximately 20.48 hours per day.

Step-by-step solution

- Identify Given Information

Extract the given values: Well's pump rate is 250 gallons per minute (gpm), population is 1,575 people, and the average water usage is 195 gallons per capita per day (gpcd).

- Convert Per Capita Daily Usage to Total Daily Demand

To find the total daily demand, multiply the population by the average gpcd. Total Daily Demand = Population × Average gpcdTotal Daily Demand = 1,575 × 195 = 307,125 gallons per day

- Calculate Total Pumping Time Needed

First, convert the well's pump rate to gallons per day: Well's pump rate = 250 gpm × 60 minutes/hour = 15,000 gallons per hourNext, calculate the number of hours the well must run to meet the total daily demand using the formula: Hours per day = Total Daily Demand / Pump Rate per Hour Hours per day = 307,125 / 15,000 ≈ 20.475 hours per day.

- Interpret the Result

The well must run approximately 20.48 hours per day to meet the average daily demand of the population.

Key concepts

Water Demand Estimation

When dealing with water systems, one of the first steps is to estimate the water demand. This involves calculating the total amount of water a population needs daily.
To start, you need two key pieces of information: the population size and the average water usage per person per day (usually given as gallons per capita per day, or gpcd). Here’s the formula you use: Total Daily Demand = Population × Average gpcd.
For example, if you have a population of 1,575 people and each person uses an average of 195 gallons per day, then:

• Total Daily Demand = 1,575 people × 195 gpcd = 307,125 gallons per day

Always ensure you have the correct units and accurate values to get an accurate estimate. This calculation helps water system planners and engineers ensure they can meet the daily water needs of a community.

Pumping Rate Calculations

Once the total daily water demand is known, the next step is to determine how often a well or pump must operate to meet this demand.
First, you need the pump's rate, typically given in gallons per minute (gpm). To find out how many gallons the pump can deliver in an hour, multiply by 60 (the number of minutes in an hour).
For example, a pump with a rate of 250 gpm would pump:

• 250 gpm × 60 minutes = 15,000 gallons per hour

Now, use this hourly pumping rate to calculate how many hours the well needs to run per day. The formula is:
Hours per Day = Total Daily Demand / Pump Rate per Hour.
With a daily demand of 307,125 gallons and a pump rate of 15,000 gallons per hour, the calculation is:

• Hours per Day = 307,125 gallons per day / 15,000 gallons per hour ≈ 20.48 hours per day

This means the well must run for about 20.48 hours every day to supply enough water for the population.

Convert Units in Water Management

In water management, converting units is crucial for making accurate calculations.
Conversions often involve changing small units (like gallons per minute) to larger ones (like gallons per day). Here's a common scenario:
Convert a pump rate from gpm to gallons per day:

• First, convert the gpm to gallons per hour by multiplying by 60 (since there are 60 minutes in an hour).
• For example, 250 gpm × 60 minutes = 15,000 gallons per hour.

Next, convert the hourly rate to a daily rate by multiplying by 24 (the number of hours in a day):

• 15,000 gallons per hour × 24 hours = 360,000 gallons per day

Remember, accurate unit conversion is key in obtaining correct results in water demand and supply calculations.
By mastering these unit conversions, you can handle more complex water management problems with ease.