Question

A drainage channel has a 10 -foot weir and a weir overflow rate of 7 gpm/ft. What is the daily flow expressed in MGD?

Short answer

0.1008 MGD

Step-by-step solution

Calculate Total Flow Rate

Multiply the weir length by the weir overflow rate to find the total flow rate. \[ \text{Total Flow Rate} = \text{Weir Length} \times \text{Weir Overflow Rate} = 10 \text{ ft} \times 7 \text{ gpm/ft} = 70 \text{ gpm} \]

Convert Gallons per Minute to Gallons per Day

Convert the total flow rate from gallons per minute (gpm) to gallons per day (gpd). There are 1440 minutes in a day. \[ \text{Total Flow Rate} = 70 \text{ gpm} \times 1440 \text{ minutes/day} = 100,800 \text{ gpd} \]

Convert Gallons per Day to Million Gallons per Day

Convert the total flow from gallons per day (gpd) to million gallons per day (MGD). \[ \text{Total Flow Rate} = \frac{100,800 \text{ gpd}}{1,000,000} = 0.1008 \text{ MGD} \]

Key concepts

weir overflow rate

The weir overflow rate is a measurement used to determine the flow rate of water over a weir per unit length. For example, in the provided exercise, the weir overflow rate is 7 gallons per minute per foot (gpm/ft). This means for every foot of the weir, 7 gallons of water flow over it every minute.

To find the total flow rate of the water passing over the weir, you need to multiply the length of the weir by the weir overflow rate. Here's the basic formula: \[ \text{Total Flow Rate} = \text{Weir Length} \times \text{Weir Overflow Rate} \]

Using the example:

• The weir length is 10 ft
• The weir overflow rate is 7 gpm/ft

This gives us: \[ \text{Total Flow Rate} = 10 \text{ ft} \times 7 \text{ gpm/ft} = 70 \text{ gpm} \]
Understanding this concept is critical for determining water management in channels and drainage systems. It helps ensure the flow rate is within permissible limits to prevent overflow and flooding.

flow rate conversion

Flow rate conversion allows us to compare and utilize flow measurements in different units. For example, converting the flow rate from gallons per minute (gpm) to gallons per day (gpd). This is necessary for various calculations in water management, where daily flow rates are a more comprehensive measure compared to minute-based rates.

There are 1440 minutes in a day, thus: \[ \text{Gallons per day (gpd)} = \text{Gallons per minute (gpm)} \times 1440 \text{ minutes per day} \]
To convert the previously calculated flow rate of 70 gpm to gpd, use the formula: \[ \text{Total Flow Rate} = 70 \text{ gpm} \times 1440 \text{ minutes/day} = 100,800 \text{ gpd} \]
This ensures you understand how much water is flowing through in a full day, making it easier to manage and plan water usage, drainage requirements, or storage capacities.

gallons per minute to gallons per day

In many fields, especially in water management, it is essential to convert gallons per minute (gpm) to gallons per day (gpd). This conversion allows for better planning and management over extended periods.

To perform this conversion, remember that there are 1440 minutes in a day. Here’s the easy step-by-step method to convert gpm to gpd:

• Find the total flow rate in gpm
• Multiply by the number of minutes in a day (1440) to get gpd

For example, if the flow rate is 70 gpm:

\[ \text{Total Flow Rate} = 70 \text{ gpm} \times 1440 \text{ minutes/day} = 100,800 \text{ gpd} \]
This result tells us that 70 gallons per minute equate to 100,800 gallons in one day. Calculating this helps in understanding the volume of water passing through in a day, useful in designing systems for water management, storage solutions, and daily usage metrics. It is a straightforward but powerful conversion that simplifies water flow management.