How to Calculate and Solve for Weir Discharge | Methods of Application of Water

September 29, 2020April 18, 2024 Loveth Idoko

Last Updated on April 18, 2024

The image above represents weir discharge. To calculate weir discharge, three essential parameters are needed and these parameters are Co-efficient of weir (C), Length of the weir (L) and Head of water over the crest (H).

The formula for calculating weir discharge:

Q = CLH^1.5

Where:

Q = Weir Discharge
C = Co-efficient of Weir
L = Length of the Weir
H = Head of Water over the Crest

Let’s solve an example;
Find the weir discharge when the co-efficient of weir is 14, the lenght of the weir is 22 and the head of water over the crest is 8.

This implies that;

C = Co-efficient of Weir = 14
L = Length of the Weir = 22
H = Head of Water over the Crest = 8

Q = CLH^1.5
That is, Q = (14)(22)(8)^1.5
Q = (14)(22)(22.62)
Q = 6969.2

Therefore, the weir discharge is 6969.2.

Calculating for the Co-efficient of Weir when the Weir Discharge, the Length of the Weir and the Head of Water over the Crest are Given

C = ^Q / _LH^1.5

Where;

C = Co-efficient of Weir
Q = Weir Discharge
L = Length of the Weir
H = Head of Water over the Crest

Let’s solve an example;
Find the co-efficient of weir when the weir discharge is 40, the length of the weir is 14 and the head of water over the crest is 8.

This implies that;

Q = Weir Discharge = 40
L = Length of the Weir = 14
H = Head of Water over the Crest = 8

C = ^Q / _LH^1.5
C = ⁴⁰ / _{14 x 8^1.5}
Then, C = ⁴⁰ / _{14 x 22.62}
C = ⁴⁰ / _316.68
C = 0.126

Therefore, the co-efficient of weir is 0.126.

Calculating for the Length of the Weir when the Weir Discharge, the Co-efficient of Weir and the Head of Water over the Crest are Given

L = ^Q / _CH^1.5

Where;

L = Length of the Weir
Q = Weir Discharge
C = Co-efficient of Weir
H = Head of Water over the Crest

Let’s solve an example;
Find the length of the weir when the weir discharge is 24, the co-efficient of weir is 10 and the head of water over the crest is 2.

This implies that;

Q = Weir Discharge = 24
C = Co-efficient of Weir = 10
H = Head of Water over the Crest = 2

L = ^Q / _CH^1.5
That is, L = ²⁴ / _{10 x 2^1.5}
L = ²⁴ / _28.2
L = 0.851

Therefore, the length of the weir is 0.851.

Calculating for the Head of Water over the Crest when the Weir Discharge, the Co-efficient of Weir and the Length of the Weir are Given

H = ^1.5√ (^Q / _CL)

Where;

H = Head of Water over the Crest
Q = Weir Discharge
C = Co-efficient of Weir
L = Length of the Weir

Let’s solve an example;
Find the head of water over the crest when the weir discharge is 30, the co-efficient of weir is 5 and the length of the weir is 4.

This implies that;

Q = Weir Discharge = 30
C = Co-efficient of Weir = 5
L = Length of the Weir = 4

H = ^1.5√ (^Q / _CL)
H = ^1.5√ (³⁰ / _{5 x 4})
So, H = ^1.5√ (³⁰ / ₂₀)
H = ^1.5√ 1.5
H = 1.31

Therefore, the head of water over the crest is 1.31.

How to Calculate Weir Discharge With Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the weir discharge.

To get the answer and workings of the weir discharge 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 Agricultural under Engineering.

Now, Click on Methods of Application of Water under Agricultural

Now, Click on Weir Discharge under Methods of Application of Water

The screenshot below displays the page or activity to enter your values, to get the answer for the weir discharge according to the respective parameters which is the Co-efficient of weir (C), Length of the weir (L) and Head of water over the crest (H).

Now, enter the values appropriately and accordingly for the parameters as required by the Co-efficient of weir (C) is 14, Length of the weir (L) is 22 and Head of water over the crest (H) is 8.

Finally, Click on Calculate

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