The image above represents stage discharge extension. To calculate stage discharge extension, four essential parameters are needed, and these parameters are Area of Cross-Section (A), Roughness Co-efficient (c), Hydraulic Radius (R) and Slope in (%) of the Energy Line (s).
The formula for calculating stage discharge extension.
Q = Ac√(Rs)
Where:
Q = Stage Discharge Extension
A = Area of Cross-Section
c = Roughness Co-efficient
R = Hydraulic Radius
s = Slope in (%) of the Energy Line
Let’s solve an example;
Find the stage discharge extension when the area of cross-section is 12, the roughness co-efficient is 16, the hydraulic radius is 13 and the slope in (%) of the energy line is 11.
This implies that;
A = Area of Cross-Section 12
c = Roughness Co-efficient = 16
R = Hydraulic Radius = 13
s = Slope in (%) of the Energy Line = 11
Q = Ac√(Rs)
Q = 12(16)√(13(11))
That is, Q = 192√(143)
Q = 192(11.95)
Q = 2295.9
Therefore, the stage discharge extension is 2295.9.
Calculating the Area of Cross-Sectional when the Stage Discharge Extension, the Roughness Co-efficient, the Hydraulic Radius and the Slope in (%) of the energy line are Given
A = Q / c √RS
Where;
A = Area of Cross-Section
Q = Stage Discharge Extension
c = Roughness Co-efficient
R = Hydraulic Radius
s = Slope in (%) of the Energy Line
Let’s solve an example;
Find the area of cross-section when the stage discharge extension is 14, the roughness co-efficient is 10, the hydraulic radius is 9 and the slope in (%) of the energy line is 5.
Master Every Calculation Instantly
Unlock solutions for every math, physics, engineering, and chemistry problem with step-by-step clarity. No internet required. Just knowledge at your fingertips, anytime, anywhere.
This implies that;
Q = Stage Discharge Extension = 14
c = Roughness Co-efficient = 10
R = Hydraulic Radius = 9
s = Slope in (%) of the Energy Line = 5
A = Q / c √RS
A = 14 / 10 √(9)(5)
Then, A = 14 / 10 (6.70)
A = 14 / 67
A = 0.208
Therefore, the area of cross-section is 0.208.
Read more:Â How to Calculate and Solve for Expected Discharge | Flood Formulae | Irrigation Water Requirement
Calculating the Roughness Co-efficient when the Stage Discharge Extension, Area of Cross-Sectional, the Hydraulic Radius and the Slope in (%) of the energy line are Given
c = Q / A √RS
Where;
c = Roughness Co-efficient
Q = Stage Discharge Extension
A = Area of Cross-Section
R = Hydraulic Radius
s = Slope in (%) of the Energy Line
Let’s solve an example;
Find the roughness co-efficient when the stage discharge extension is 32, the area of cross-section is 10, the hydraulic radius is 20, and the slope in (%) of the energy line is 5.
This implies that;
Q = Stage Discharge Extension = 32
A = Area of Cross-Section = 10
R = Hydraulic Radius = 20
s = Slope in (%) of the Energy Line = 5
c = Q / A √RS
So, c = 32 / 10 √(20)(5)
c = 32 / 10 √100
c = 32 / 10 (10)
That is, c = 32 / 10
c = 3.2
Therefore, the roughness co-efficient is 3.2.
Calculating the Hydraulic Radius when the Stage Discharge Extension, Area of Cross-Sectional, the Roughness Co-efficient and the Slope in (%) of the energy line are Given
R = (Q / Ac)2 / S
Where;
R = Hydraulic Radius
Q = Stage Discharge Extension
A = Area of Cross-Section
c = Roughness Co-efficient
s = Slope in (%) of the Energy Line
Let’s solve an example;
Find the hydraulic radius when the stage discharge extension is 40, the area of cross-section is 8, the roughness co-efficient is 4 and the slope in (%) of the energy line is 4.
This implies that;
Q = Stage Discharge Extension = 40
A = Area of Cross-Section = 8
c = Roughness Co-efficient = 4
s = Slope in (%) of the Energy Line = 4
R = (Q / Ac)2 / S
So, R = (40 / 8 x 4)2 / 4
R = (40 / 32)2 / 4
R = (1.25)2 / 4
That is, R = 1.5625 / 4
R = 0.14
Therefore, the hydraulic radius is 0.14.
Calculating the Slope in (%) of the energy line when the Stage Discharge Extension, Area of Cross-Sectional, the Roughness Co-efficient and the Hydraulic Radius are Given
S = (Q / Ac)2 / R
Where;
s = Slope in (%) of the Energy Line
Q = Stage Discharge Extension
A = Area of Cross-Section
c = Roughness Co-efficient
R = Hydraulic Radius
Let’s solve an example;
Find the slope in (%) of the energy line when the stage discharge extension is 30, the area of cross-section is 12, the roughness co-efficient is 6 and the hydraulic radius is 2.
This implies that;
Q = Stage Discharge Extension = 30
A = Area of Cross-Section = 12
c = Roughness Co-efficient = 6
R = Hydraulic Radius = 2
S = (Q / Ac)2 / R
S = (30 / 12 x 6)2 / 2
Then, S = (0.416)2 / 2
S = 0.173056 / 2
S = 0.086
Therefore, the slope in (%) of the energy line is 0.086.
How to Calculate Stage Discharge Extension Using Nickzom
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the stage discharge extension.
To get the answer and workings of the stage discharge extension 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 Irrigation Water Requirement under Agricultural
Now, Click on Stage Discharge Extension under Irrigation Water Requirement
The screenshot below displays the page or activity to enter your values, to get the answer for the stage discharge extension according to the respective parameters which is the Area of Cross-Section (A), Roughness Co-efficient (c), Hydraulic Radius (R) and Slope in (%) of the Energy Line (s).
Now, enter the values appropriately and accordingly for the parameters as required by the Area of Cross-Section (A) is 12, Roughness Co-efficient (c) is 16, Hydraulic Radius (R) is 13 and Slope in (%) of the Energy Line (s) is 11.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the stage discharge extension and presents the formula, workings and steps too.
