How to Calculate and Solve for Storage Co-efficient for a Confined Aquifer | Water Budget

Last Updated on March 30, 2024

The image above represents storage co-efficient for a confined aquifer. To calculate storage co-efficient for a confined aquifer, five essential parameters are needed, and these parameters are Unit Weight of Water (γ_w), Confined Aquifer Thickness (H), Compressibility of the Aquifer Material (α), Porosity of Aquifer Material (n) and Compressibility of Water (β).

The formula for calculating storage co-efficient for a confined aquifer:

S = γ_w(α + nβ)H

Where;

S = Storage Co-efficient for a Confined Aquifer
γ_w = Unit Weight of Water
H = Confined Aquifer Thickness
α = Compressibility of the Aquifer Material
n = Porosity of Aquifer Material
β = Compressibility of Water

Let’s solve an example;
Find the storage co-efficient for a confined aquifer when the unit weight of water is 8, confined aquifer thickness is 12, the compressibility of the aquifer material is 21, the porosity of aquifer material is 18 and the compressibiity of water is 14.

This implies that;

γ_w = Unit Weight of Water = 8
H = Confined Aquifer Thickness = 12
α = Compressibility of the Aquifer Material = 21
n = Porosity of Aquifer Material = 18
β = Compressibility of Water = 14

S = γ_w(α + nβ)H
S = 8(21 + 18(14))12
That is, S = 8(21 + 252)12
S = 8(273)12
S = 26208

Therefore, the storage co-efficient for a confined aquifer is 26208.

Calculating the Unit Weight of Water when the Storage Co-efficient for a Confined Aquifer, the Confined Aquifer Thickness, the Compressibility of the Aquifer Material, the Porosity of Aquifer Material and the Compressibility of Water are Given

γ_w = ^S / _{(a + nβ)H}

Where;

γ_w = Unit Weight of Water
S = Storage Co-efficient for a Confined Aquifer
H = Confined Aquifer Thickness
α = Compressibility of the Aquifer Material
n = Porosity of Aquifer Material
β = Compressibility of Water

Let’s solve an example;
Find the unit weight of water when the storage co-efficient for a confined aquifer is 20, the confined aquifer thickness is 10, the compressibility of the aquifer material is 8, the porosity of aquifer material is 3 and the compressibility of water is 4.

This implies that;

S = Storage Co-efficient for a Confined Aquifer = 20
H = Confined Aquifer Thickness = 10
α = Compressibility of the Aquifer Material = 8
n = Porosity of Aquifer Material = 3
β = Compressibility of Water = 4

γ_w = ^S / _{(a + nβ)H}
Then, γ_w = ²⁰ / _{(8 + (3 x 4))10}
γ_w = ²⁰ / _{(8 + 12)10}
γ_w = ²⁰ / ₍₂₀₎₁₀
So, γ_w = ²⁰ / ₂₀₀
γ_w = 0.1

Therefore, the unit weight of water is 0.1.

Read more: How to Calculate and Solve for Discharge Current | Unconfined Aquifer | Water Budget

Calculating the Confined Aquifer Thickness when the Storage Co-efficient for a Confined Aquifer, the Unit Weight of Water, the Compressibility of the Aquifer Material, the Porosity of Aquifer Material and the Compressibility of Water are Given

H = ^S / _{γw(a + nβ)}

Where;

H = Confined Aquifer Thickness
S = Storage Co-efficient for a Confined Aquifer
γ_w = Unit Weight of Water
α = Compressibility of the Aquifer Material
n = Porosity of Aquifer Material
β = Compressibility of Water

Let’s solve an example;
Find the Confined Aquifer thickness when the storage co-efficient for a confined aquifer is 12, the unit weight of water is 8, the compressibility of the aquifer material is 7, the porosity of aquifer material is 14 and the compressibility of water is 9.

This implies that;

S = Storage Co-efficient for a Confined Aquifer = 12
γ_w = Unit Weight of Water = 8
α = Compressibility of the Aquifer Material = 7
n = Porosity of Aquifer Material = 14
β = Compressibility of Water = 9

H = ^S / _{γw(a + nβ)}
That is, H = ¹² / _{8(7 + (14 x 9))}
H = ¹² / _{8(7 + 126)}
H = ¹² / ₈₍₁₃₃₎
So, H = ¹² / ₁₀₆₄
H = 0.011

Therefore, the confined aquifer thickness is 0.011.

Calculating the Compressibility of the Aquifer Material when the Storage Co-efficient for a Confined Aquifer, Unit Weight of Water, Confined Aquifer Thickness, the Porosity of Aquifer Material and the Compressibility of Water are Given

α = (^S / _γwH) – nβ

Where;

α = Compressibility of the Aquifer Material
S = Storage Co-efficient for a Confined Aquifer
γ_w = Unit Weight of Water
H = Confined Aquifer Thickness
n = Porosity of Aquifer Material
β = Compressibility of Water

Let’s solve an example;
Find the compressibility of the aquifer material when the storage co-efficient for a confined aquifer is 30, the unit weight of water is 10, the confined aquifer thickness is 5, the porosity of aquifer material is 5 and the compressibility of water is 2.

This implies that;

S = Storage Co-efficient for a Confined Aquifer = 30
γ_w = Unit Weight of Water = 10
H = Confined Aquifer Thickness = 5
n = Porosity of Aquifer Material = 5
β = Compressibility of Water = 2

α = (^S / _γwH) – nβ
α = (³⁰ / _{10 x 5}) – (5 x 2)
Then, α = (³⁰ / ₅₀) – 10
α = 0.6 – 10
α = – 9.4

Therefore, the compressibility of the aquifer material is – 9.4.

Read more: How to Calculate and Solve for Entrance Velocity | Darcy’s Law | Water Budget

Calculating the Porosity of Aquifer Material when the Storage Co-efficient for a Confined Aquifer, the Unit Weight of Water, the Confined Aquifer Thickness, the Compressibility of the Aquifer Material and the Compressibility of Water are Given

n = ^{(S / _γwH) – α} / _β

Where;

n = Porosity of Aquifer Material
S = Storage Co-efficient for a Confined Aquifer
γ_w = Unit Weight of Water
H = Confined Aquifer Thickness
α = Compressibility of the Aquifer Material
β = Compressibility of Water

Let’s solve an example;
Find the porosity of aquifer material when the storage co-efficient for a confined aquifer is 30, the unit weight of water is 4, the confined aquifer thickness is 3, the compressibility of the aquifer material is 10 and the compressibility of water is 6.

This implies that;

S = Storage Co-efficient for a Confined Aquifer = 30
γ_w = Unit Weight of Water = 4
H = Confined Aquifer Thickness = 3
α = Compressibility of the Aquifer Material = 10
β = Compressibility of Water = 6

n = ^{(S / _γwH) – α} / _β
That is, n = ^{(30 / _{4 x 3}) – 10} / ₆
n = ^{(30 / ₁₂) – 10} / ₆
n = ^{2.5 – 10} / ₆
So, n = ^{– 7.5} / ₆
n = – 1.25

Therefore, the porosity of aquifer material is – 1.25.

Calculating the Compressibility of Water when the Storage Co-efficient for a Confined Aquifer, the Unit Weight of Water, the Confined Aquifer Thickness, the Compressibility of the Aquifer Material and the Porosity of Aquifer Material are Given

β = ^{(S / _γwH) – α} / _n

Where;

β = Compressibility of Water
S = Storage Co-efficient for a Confined Aquifer
γ_w = Unit Weight of Water
H = Confined Aquifer Thickness
α = Compressibility of the Aquifer Material
n = Porosity of Aquifer Material

Let’s solve an example;
Find the compressibility of water when the storage co-efficient for a confined aquifer is 20, the unit weight of water is 12, the confined aquifer thickness is 2, the compressibility of the aquifer material is 6 and the porosity of aquifer material is 4.

This implies that;

S = Storage Co-efficient for a Confined Aquifer = 20
γ_w = Unit Weight of Water = 12
H = Confined Aquifer Thickness = 2
α = Compressibility of the Aquifer Material = 6
n = Porosity of Aquifer Material = 4

β = ^{(S / _γwH) – α} / _n
This means, β = ^{(20 / _{12 x 2}) – 6} / ₄
β = ^{(20 / ₂₄) – 6} / ₄
β = ^{0.83 – 6} / ₄
So, β = ^{– 5.16} / ₄
β = – 1.291

Therefore, the compressibility of water is – 1.291.

How to Calculate Storage Co-efficient for a Confined Aquifer Using Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the storage co-efficient for a confined Aquifer.

To get the answer and workings of the storage co-efficient for 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 1,500 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 Agricultural under Engineering.

Now, Click on Water Budget under Agricultural

Now, Click on Storage Co-efficient for a confined Aquifer under Water Budget

The screenshot below displays the page or activity to enter your values, to get the answer for the storage co-efficient for a confined aquifer according to the respective parameters which are the Unit Weight of Water (γ_w), Confined Aquifer Thickness (H), Compressibility of the Aquifer Material (α), Porosity of Aquifer Material (n) and Compressibility of Water (β).

Now, enter the values appropriately and accordingly for the parameters as required by the Unit Weight of Water (γ_w) is 8, Confined Aquifer Thickness (H) is 12, Compressibility of the Aquifer Material (α) is 21, Porosity of Aquifer Material (n) is 18 and Compressibility of Water (β) is 14.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the storage co-efficient for a confined aquifer and presents the formula, workings and steps too.