Lesson 3: Introduction to Water Treatment Math
Water Demand
Introduction The rest of this lesson will focus on water demand, the volume of water required by users to satisfy their needs. Water demand will vary from location to location and from day to day within a location. Demand will also depend on the time of day (as shown below), the day of the week, the season of the year, prevailing weather conditions, manufacturing demands, and unusual events such as fires or mains breaks.
Using the water demand for a region, we can determine the required size of the water plant, storage tanks, and distribution system components. Below, we have listed the factors we will use to size each component. The factors themselves will be explained in later sections. • •
Capacity of pumps and plants - based on maximum daily water demand Capacity of distribution pipes - based on the maximum hourly water demand
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Fire storage volume - based on expected fire flow and duration
Average Daily Water Demand You may remember from the last lesson that the average daily water use is 100 gallons per person per day. Although this is a good, simple rule of thumb, the value takes into account only residential uses of water. In most situations, a water plant will supply residential, commercial, industrial, and public water. So the average daily water demand (the average amount of water used daily per person excluding fire fighting) for most regions will be much greater, ranging from 120 to 300 gallons per person per day. Average daily water demand for various regions in the United States is shown on the map below. Demand is reported in gpcd or gallons per capita day, which means the number of gallons of water used per person per day.
The map only shows general regional values. Average daily water demand can be much less or much more than that shown on the map and will depend on the specific situation. The best way to calculate average daily water demand is to compare the community in question to a community of similar size and type in the region. Rural communities, for example, tend to use water merely or primarily for residential purposes, so the water demand is much lower than in urban areas, and can often be as low as 100 gpcd.
The average daily water demand is sized to the community using the following equation: Average community daily water demand = Average daily water demand × Number of people
Plant and Distribution System Capacity In order to find the capacity of the treatment plant, we must calculate another factor - the maximum daily water demand, which is the greatest amount of water which will be asked for by the users in one day. The maximum daily water demand is calculated as follows: Maximum daily water demand = 1.8 × (Average community daily water demand)
We will also need to calculate the maximum hourly water demand. This factor takes into account the daily cycles of water use. At any given time, up to three times the average daily water demand will be used, so the maximum hourly water demand is calculated as follows: Maximum hourly water demand = 3 × (Average community daily water demand)
Example Let's consider a situation in which a water treatment plant in the Rio Grande Region is being planned to serve 40,000 people. At the moment, we will consider water demand excluding fire fighting. What should the capacity of the plant and distribution system be? The first step is to find the average daily water demand on the map. The value for the Rio Grande Region is 278 gpcd. Then this value is translated into average community daily water demand in the following way: 278 gal/(person day) × 40,000 people = 11.1 MGD
You will notice that we converted from gal/day to MGD to make the answer more understandable. 11.1 MGD is the average community daily water demand for the facility. In order to determine the required capacity of the water plant, we must calculate the maximum daily water demand. This value is calculated as follows:
1.8 × 11.1 MGD = 20.0 MGD
This value determines the the size of the water treatment plant. The water treatment plant must have the capacity to treat 20.0 MGD in order to support peak demands. Finally, the maximum hourly water demand is calculated as follows: 3 × 11.1 MGD = 33.3 MGD
While the maximum daily water demand is used to size the treatment facility, the maximum hourly water demand should be used to size the distribution system. The distribution system should be of an adequate size to carry 33.3 MGD.
Fire Flow Introduction As you will remember from the last lesson, water treatment plants are sized to deal with the amount of water used by fire fighters, the fire flow, as well as for residential and industrial customers. The total flow of the plant is defined as follows: Total flow = Maximum daily water demand + Fire flow
The total flow is the total amount of water that the water plant has available. This will include the capacity of the plant and of any storage structures. In most cases, the treatment plant can be sized to merely deal with the maximum daily demand as long as the storage facility is large enough to deal with fire flows.
Calculating Fire Flow The fire flow for a region can be calculated in a variety of ways. Most methods require a knowledge of the size and type of buildings within the distribution system. We will use a simple method which is simply based on the population of the community. The fire flow is calculated as follows: Fire flow (gpm) =
Where "P" is the population in 1,000's of people. So, for our community with a population of 40,000, the fire flow would be:
Duration of Flow Unlike the residential water demand, water demand for fire fighting typically last only short periods of time. For insurance purposes the required length of time we should expect fire flow to last is calculated as follows:
Using the fire flow value calculated above, the duration would be:
Volume The required storage capacity for fire flow is calculated as follows: Capacity = Fire flow × Duration After converting the duration to minutes, we can plug our values into the equation: Capacity = 6,043 gpm × 360 minutes Capacity = 2,175,480 gal
The storage tank must thus have a fire flow capacity of 2.2 million gallons, added to any other required volumes (for chemical contact time, emergency use, etc.)
Review This lesson introduces you to a variety of resources you will find helpful while learning and using water treatment math. Then, in the second half of the lesson, we learn to calculate average daily community water demand, maximum daily water demand, maximum hourly water demand, and fire flow amount and duration. These figures allow us to size various components of the water treatment system, as follows: • • •
water treatment plant capacity - based on maximum daily water demand distribution system capacity - based on maximum hourly water demand fire storage volume - based on fire flow and duration.
New Formulas Used Average community daily water demand: Average community daily water demand = Average daily water demand × Number of people
Maximum daily water demand: Maximum daily water demand = 1.8 × (Average community daily water demand)
Maximum hourly water demand: Maximum hourly water demand = 3 × (Average community daily water demand)
Total amount of water the plant has available: Total flow = Maximum daily water demand + Fire flow
Fire flow: Fire flow (gpm) =
Duration of fire flow:
Storage tank capacity for fire flow: Capacity = Fire flow × Duration
Assignment 1. Read section A.9 on pages 642 to 643 in Volume 1 of your text. 2. Answer the following questions. Show all of your work and circle the answer for each math problem below. If there is insufficient information to find the answer, write "Insufficient information". When you are done, either email, mail or fax the assignment to your instructor. 1. 3 inches of mercury are equivalent to how many inches of water? 2. You have a bucket containing 5 gallons of water. How many cubic feet of water are there in the bucket? 3. How much does the water in the bucket above weigh? 4. A water plant is being built to serve a community of 500,000 people with an average daily water demand of 200 gpd. What is the average daily water demand, excluding fire fighting, of the community? 5. Which value should be used to size the distribution system? 6. Which value should be used to size the treatment plant? 7. What is the fire flow for the treatment plant? 8. What duration of fire flow should be used for insurance purposes? 9. What is the required storage volume for the fire flow water? 10. What is the treatment plant's total flow?
