# Sewer Math

Quote of the Day

A startup is a temporary organization searching for a repeatable and scalable business model.

— Steve Blank

## Introduction

Figure 1: My Friend, Lloyd Wander, Made a Good Business Out of Fixing Manhole Cover Problems (Photo).

A good friend of mine is an entrepreneur and I caught him doing some math the other day. While it was simply basic arithmetic, it shows that kind of reasoning that people need to do in their daily work every day.

It is useful to go through this simple exercise because you can see how a businessman goes about understanding his market and how to serve it. Most entrepreneurs also have to be salesmen and my friend is a master at sales.

He tells me that there are three types of salesman ? he assigns letter grades:

1. (A) Visionary

This salesman explains how a companies products and strategies can change your life. He explains how what they do can reduce your costs, make you more productive, create opportunities and in general can make your life better.

2. (B) Presenter

This salesman understands their product line and will explain all the products that they have available. They will tell you things such as which products are most popular and which products are better for relative to one another. This is the most common type of salesman.

3. (C) Order Taker

This salesman simply takes your order. He does not present you any options and simple is there to process your request. Think of the person working the drive-up window at McDonalds.

My friend always strives to be a type "A" salesman. He started a company that makes and installs high-quality water seals for manhole covers -- the round, iron discs that you see providing sewer access (Figure 1). In order to sell people on his product, he needed to find a way to show them that not sealing their manhole covers well is costing them money. This blog post explains how he went about showing his customers the value of his product to them.

Since I like Fermi problems, I will also go through how to estimate the number of manhole covers in a city and the amount of sewage that a city must deal with. These kinds of calculations are important to his business because they tell him his Total Addressable Market (TAM) (number of manhole covers) and how much fresh water leakage is occurring in the system (expected amount of sewage versus actual).

## Background

### Sewer Economics

Let's discuss the economics of sewers and how this economics affects municipalities:

1. Cities pay for sewer treatment on a per gallon basis.

If the sewage is diluted with rainwater, they pay the same amount per gallon as if it were not diluted.

2. Leaking manhole covers can cost the city an enormous amount of money.

Even a small city can have thousands of manhole covers (e.g. Champlin, MN has 216 manholes and a population of 24000) . If they leak, the inflow of clean rainwater into the sewers can be enormous. Typical treatment costs run about \$2 per 1000 gallons of sewage. Adding rain water to sewage just adds to your costs.

3. Installing a gasket on the sewer manhole is relatively cheap.

This means that a city that seals up its manholes from rain can realize a quick return on its investment.

### Surface Water Ingress to a Sewer

If the manhole cover leaks, it can allow clean rainwater to get into the sewage and the city will end up paying to cleanup more water than it needs to. These "leaks" can be massive -- this one put 700,000 gallons of rainwater into one city's system.

## Analysis

I will discuss three problems. The first problem, the cost of a leaky manhole cover, is the one my friend focuses on. This calculation uses the number of manhole covers in the city and the total sewage flow, for which I also provide estimates.

### Cost of Each Leaky Manhole Cover

The key argument for sealing leaky manholes is that you will save money in the long run. My friends approach to this problem is simple:

• Determine the sewage flow for the city on dry days.
• Determine the sewage flow for the cit on wet days.
• Determine the amount of clean water flowing into their sewage system by taking the difference between these numbers. This water enters the sewer through a water flow sensor. To learn more about water flow sensors, head to the Flow Meters website.
• Determine the cost of treating that clean water.
• Determine the average cost of a leaky manhole by dividing the treatment cost by the number of manholes.

If the average cost of leaky manhole is significantly more than the cost of putting a seal on it, then it is worthwhile for the city to seal their manholes better.

There are some issues with the analysis. For example, some residents of the city may pump that sump water into the city sewer (this is illegal in my city). But on average, his analysis is probably reasonable.

### Sewage Generation for a Small Town

Figure 2 shows my estimate for the expected sewage flow from Champlin, Minnesota (a city with excellent sewer documentation). Note how my estimate is lower than their actual flow. They may getting fresh water inflow. It would be very interesting to look the differences in flow rates between dry days and rainy days. I do not have access to that data.

Figure 2: Estimate of the Total Sewage Volume Per Day.

### Number of Manholes in a Small Town

Figure 3 shows two approaches for estimating the number of manholes in a city. I used the city of Champlin, Minnesota for my example. They have excellent sewer system documentation that provided me actual data for verification of the accuracy of my estimates.

Figure 3: Estimating the Number of Manhole Covers in a City.

## Conclusion

Just a quick post to illustrate the kind of calculation that a small business manager might do regularly. What I find the most interesting about this little bit of arithmetic is how valuable that city managers found the information and how they were able to use the information to justify upgrading their manhole covers.

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### 4 Responses to Sewer Math

1. CC says:

Of course, in a city where storm drains are tied in to municipal wastewater, your friend won't get anywhere 🙂

• mathscinotes says:

You are correct. He does most of his business in Florida, where they keep the storm drains and waste water separate. I am amazed at the amount of business he has done. They make their seals out of a two-part, epoxy-like resin that they put in place out in the field. It was interesting to see how they do it.

mathscinote

• CC says:

It's sensible to keep them separate. Cities where they're combined, well, every big storm they're at risk of overflowing or undertreating or both. It's not easy to separate miles and miles of tunnels, either...

2. James Hu says:

You say very good. Hope we can become A type for the manhole cover business in future.