How to Calculate and Solve for Steady Flow in a Confined Aquifer | Flow Lines

August 20, 2020April 7, 2024 Loveth Idoko

Last Updated on April 7, 2024

The image above represents steady flow in a confined aquifer. To calculate steady flow in a confined aquifer, three essential parameters are needed and these parameters are Hydraulic Conductivity (K), Aquifer Thickness (L) and Hydraulic Gradient or Slope of Potentiometric Surface (^dh/_dl).

The formula for calculating steady flow in a confined aquifer:

q^t = KL^dh/_dl

Where:

q^t = Steady Flow in a Confined Aquifer
K = Hydraulic Conductivity
L = Aquifer Thickness
^dh/_dl = Hydraulic Gradient or Slope of Potentiometric Surface

Let’s solve an example;
Find the steady flow in a confined aquifer when the hydraulic conductivity is 22, the aquifer thickness is 18 and the hydraulic gradient is 10.

This implies that;

K = Hydraulic Conductivity = 22
L = Aquifer Thickness = 18
^dh/_dl = Hydraulic Gradient or Slope of Potentiometric Surface = 10

q^t = KL^dh/_dl
That is, q^t = (22)(18)(10)
q^t = 396(10)
q^t = 3960

Therefore, the steady flow in a confined aquifer is 3960.

Calculating the Hydraulic Conductivity when the Steady Flow in a Confined Aquifer, the Aquifer Thickness and the Hydraulic Gradient are Given

K = ^{q^t} / _{L^dh/_dl}

Where;

K = Hydraulic Conductivity
q^t = Steady Flow in a Confined Aquifer
L = Aquifer Thickness
^dh/_dl = Hydraulic Gradient or Slope of Potentiometric Surface

Let’s solve an example;
Find the hydraulic conductivity when the steady flow in a confined aquifer is 30, the aquifer thickness is 20 and the hydraulic gradient is 3.

This implies that;

q^t = Steady Flow in a Confined Aquifer = 30
L = Aquifer Thickness = 20
^dh/_dl = Hydraulic Gradient or Slope of Potentiometric Surface = 3

K = ^{q^t} / _{L^dh/_dl}
Then, K = ³⁰ / _{20 x 3}
K = ³⁰ / ₆₀
K = 0.5

Therefore, the hydraulic conductivity is 0.5.

Calculating the Aquifer Thickness when the Steady Flow in a Confined Aquifer, the Hydraulic Conductivity and the Hydraulic Gradient are Given

L = ^{q^t} / _{K^dh/_dl}

Where;

L = Aquifer Thickness
q^t = Steady Flow in a Confined Aquifer
K = Hydraulic Conductivity
^dh/_dl = Hydraulic Gradient or Slope of Potentiometric Surface

Let’s solve an example;
Find the aquifer thickness when the steady flow in a confined aquifer is 44, the hydraulic conductivity is 11 and the hydraulic gradient is 7.

This implies that;

q^t = Steady Flow in a Confined Aquifer = 44
K = Hydraulic Conductivity = 11
^dh/_dl = Hydraulic Gradient or Slope of Potentiometric Surface = 7

L = ^{q^t} / _{K^dh/_dl}
Then, L = ⁴⁴ / _{11 x 7}
L = ⁴⁴ / ₇₇
L = 0.57

Therefore, the aquifer thickness is 0.57.

Calculating the Hydraulic Gradient when the Steady Flow in a Confined Aquifer, the Hydraulic Conductivity and the Aquifer Thickness are Given

^dh/_dl = ^{q^t} / _KL

Where;

^dh/_dl = Hydraulic Gradient or Slope of Potentiometric Surface
q^t = Steady Flow in a Confined Aquifer
K = Hydraulic Conductivity
L = Aquifer Thickness

Let’s solve an example;
Find the hydraulic gradient when the steady flow in a confined aquifer is 60, the hydraulic conductivity is 15 and the aquifer thickness is 6.

This implies that;

q^t = Steady Flow in a Confined Aquifer = 60
K = Hydraulic Conductivity = 15
L = Aquifer Thickness = 6

^dh/_dl = ^{q^t} / _KL

So, ^dh/_dl = ⁶⁰ / _{15 x 6}
^dh/_dl = ⁶⁰ / ₉₀
^dh/_dl = 0.667

Therefore, the hydraulic gradient or potentiometric surface is 0.667.

How to Calculate Steady Flow in a Confined Aquifer Using Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the steady flow in a confined aquifer.

To get the answer and workings of the steady flow in a confined aquifer using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via web, you need to register and subscribe for NGN 2,000 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Geology under Add-on.

Now, Click on Flow Lines under Geology

Now, Click on Steady Flow in a Confined Aquifer under Flow Lines

The screenshot below displays the page or activity to enter your values, to get the answer for the steady flow in a confined aquifer according to the respective parameters which are the Hydraulic Conductivity (K), Aquifer Thickness (L) and Hydraulic Gradient or Slope of Potentiometric Surface (^dh/_dl).

Now, enter the values appropriately and accordingly for the parameters as required by the Hydraulic Conductivity (K) is 22, Aquifer Thickness (L) is 18 and Hydraulic Gradient or Slope of Potentiometric Surface (^dh/_dl) is 10.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the steady flow in a confined aquifer and presents the formula, workings and steps too.