Question

A well has a calculated specific capacity of 30 gpm per foot and operates at a flow rate of $1.08\mathrm{MGD}$. If the static water level is $28\mathrm{ft}$ bgs, what is the pumping level?

Short answer

The pumping level is 3 feet bgs.

Step-by-step solution

Convert Flow Rate to gpm

Convert the given flow rate from MGD (million gallons per day) to gpm (gallons per minute). Given flow rate: 1.08 MGD1 MGD = 1,000,000 gallons/day1 day = 24 hours1 hour = 60 minutesTherefore, 1 MGD = 1,000,000 / (24 * 60) gpmSo, 1.08 MGD = 1.08 * 1,000,000 / (24 * 60) gpm

Calculate Flow Rate in gpm

Evaluate the expression from Step 1 to find the flow rate in gpm.1.08 MGD = $$1.08\ast \frac{1,000,000}{24\ast 60}=1.08\ast \frac{1,000,000}{1440}=1.08\ast 694.444\text{gpm}=750\text{ gpm}$$

Use Specific Capacity to Find Drawdown

Use the formula for specific capacity: Specific Capacity = Flow rate (gpm) / Drawdown (feet)Rearrange to find the drawdown:Drawdown = Flow rate (gpm) / Specific Capacity (gpm per foot)Given the specific capacity: 30 gpm per footSo, Drawdown = 750 gpm / 30 gpm per foot

Calculate Drawdown

Evaluate the expression from Step 3:$$Drawdown=750/30\text{ feet}=25\text{ feet}$$

Determine Pumping Level

Subtract the drawdown from the static water level to find the pumping level.Static water level: 28 feet bgsPumping level = Static water level - DrawdownSo, Pumping level = 28 feet - 25 feet

Calculate Pumping Level

Evaluate the expression from Step 5:$$Pumpinglevel=28-25\text{ = 3 feet bgs}$$

Key concepts

flow rate conversion

Understanding how to convert flow rates is crucial for many water management tasks. In this context, flow rate was given in million gallons per day (MGD). However, we needed it in gallons per minute (gpm).
To convert MGD to gpm, we use the relationship:
1 MGD = 1,000,000 gallons/day.
Since there are 24 hours in a day and 60 minutes in an hour, we calculate:
1 MGD = \frac{1,000,000}{24 \times 60} gpm.
This gives us approximately 694.44 gpm per MGD.
Therefore, for our given flow rate of 1.08 MGD, we can evaluate:
$1.08\times 694.44=750\text{ gpm}$
Now the flow rate conversion is done, and we have it in the desired unit (gpm).

drawdown calculation

The drawdown is the difference in water level in a well before and after pumping. To calculate the drawdown, we use the specific capacity of the well.
The formula used here is:
Specific Capacity = $\frac{\text{Flow rate (gpm)}}{\text{Drawdown (feet)}}$.
Rearrange the formula to find the drawdown:
Drawdown = $\frac{\text{Flow rate (gpm)}}{\text{Specific Capacity (gpm per foot)}}$.
Given a specific capacity of 30 gpm per foot and a flow rate of 750 gpm, we calculate:
Drawdown = $\frac{750\text{ gpm}}{30\text{ gpm per foot}}=25\text{ feet}$.
This means that the water level drops by 25 feet due to pumping.

pumping level determination

The final step is to determine the pumping level. This is the level of water in the well during pumping.
We subtract the drawdown from the static water level, which is the level before pumping.
Given a static water level of 28 feet below ground surface (bgs) and a drawdown of 25 feet, we calculate:
Pumping Level = Static Water Level - Drawdown.
Pumping Level = 28 feet - 25 feet.
This results in 3 feet bgs.
This means, during pumping, the water level in the well will be 3 feet below the ground surface.