How to Calculate and Solve for Average Linear Velocity | Aquifer Characteristics

Last Updated on April 7, 2024

The image above represents average linear velocity. Three essential parameters are needed to calculate average linear velocity: discharge (Q), effective porosity (ne), and cross-sectional area (A).

The formula for calculating average linear velocity:

v_x = ^Q / _neA

Where:

v_x = Average Linear Velocity
Q = Discharge
n_e = Effective Porosity
A = Cross-Sectional Area

Let’s solve an example;
Find the average linear velocity when the discharge is 12, the effective porosity is 9, and the cross-sectional area is 22.

This implies that;

Q = Discharge = 12
n_e = Effective Porosity = 9
A = Cross-Sectional Area = 22

v_x = ^Q / _neA
So, v_x = ¹² / ₉₍₂₂₎
v_x = ¹² / ₁₉₈
v_x = 0.060

Therefore, the average linear velocity is 0.060 m/s.

Calculating the Discharge when the Average Linear Velocity, the Effective Porosity and the Cross-Sectional Area are Given

Q = v_x x n_e A

Where;

Q = Discharge
v_x = Average Linear Velocity
n_e = Effective Porosity
A = Cross-Sectional Area

Let’s solve an example;
Find the discharge when the average linear velocity is 22, the effective pororsity is 10 and the cross-sectional area is 14.

This implies that;

v_x = Average Linear Velocity = 22
n_e = Effective Porosity = 10
A = Cross-Sectional Area = 14

That is, Q = v_x x n_e A
Q = 22 x 10 x 14
Q = 3080

Therefore, the discharge is 3080.

Read more: How to Calculate and Solve for Total Volume Discharge per Unit Width of Aquifer | Flow Lines

Calculating the Effective Porosity when the Average Linear Velocity, the Discharge and the Cross-Sectional Area are Given

n_e = ^Q / _{vx x A}

Where;

n_e = Effective Porosity
v_x = Average Linear Velocity
Q = Discharge
A = Cross-Sectional Area

Let’s solve an example;
Find the effective porosity when the average linear velocity is 21, the discharge is 11 and the cross-sectional area is 8.

This implies that;

v_x = Average Linear Velocity = 21
Q = Discharge = 11
A = Cross-Sectional Area = 8

n_e = ^Q / _{vx x A}
n_e = ¹¹ / _{21 x 8}
Then, n_e = ¹¹ / ₁₆₈
n_e = 0.0654

Therefore, the effective porosity is 0.0654.

Calculating the Cross-Sectional Area when the Average Linear Velocity, the Discharge and the Effective Porosity are Given

A = ^Q / _{vx x ne}

Where;

A = Cross-Sectional Area
v_x = Average Linear Velocity
Q = Discharge
n_e = Effective Porosity

Let’s solve an example;
Find the cross-sectional area when the average linear velocity is 5, the discharge is 34 and the effective porosity is 4.

This implies that;

v_x = Average Linear Velocity = 5
Q = Discharge = 34
n_e = Effective Porosity = 4

A = ^Q / _{vx x ne}
That is, A = ³⁴ / _{5 x 4}
A = ³⁴ / ₂₀
A = 1.7

Therefore, the Cross-Sectional Area is 1.7.

How to Calculate Average Linear Velocity | Aquifer Characteristics Using Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the average linear velocity.

To get the answer and workings of the average linear velocity 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 Aquifer Characteristics under Geology

Now, Click on Average Linear Velocity under Aquifer Characteristics

The screenshot below displays the page or activity to enter your values, to get the answer for the average linear velocity according to the respective parameters which are the Discharge (Q), Effective Porosity (n_e) and Cross-Sectional Area (A).

Now, enter the values appropriately and accordingly for the parameters as required by the Discharge (Q) is 12, Effective Porosity (n_e) is 9 and Cross-Sectional Area (A) is 22.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the average linear velocity and presents the formula, workings and steps too.