How to Calculate and Solve for Flow Rate | Darcy’s Law | Transport Phenomena
Last Updated on October 2, 2021
The image above represents flow rate.
To compute for flow rate, four essential parameters are needed and these parameters are Permeability (K), Cross-Sectional Area (A), Change in Pressure (ΔP) and Length of Pipe (L).
The formula for calculating flow rate:
Q = KAΔP / L
Where:
Q = Flow Rate | Darcy’s Law
K = Permeability
A = Cross-sectional Area
ΔP = Change in Pressure
L = Length of Pipe
Let’s solve an example;
Find the flow rate when the permeability is 9, the cross-sectional area is 12, the change in pressure is 3 and the length of pipe is 10.
This implies that;
K = Permeability = 9
A = Cross-sectional Area = 12
ΔP = Change in Pressure = 3
L = Length of Pipe = 10
Q = KAΔP / L
Q = (9)(12)(3) / 10
Q = 324 / 10
Q = 32.4
Therefore, the flow rate is 32.4 m³/s.
Calculating the Permeability when the Flow Rate, the Cross-Sectional Area, the Change in Pressure and the Length of Pipe is Given.
K = Q x L / AΔP
Where:
K = Permeability
Q = Flow Rate | Darcy’s Law
A = Cross-sectional Area
ΔP = Change in Pressure
L = Length of Pipe
Let’s solve an example;
Find the permeability when the flow rate is 14, the cross-sectional area is 4, the change in pressure is 7 and the length of pipe is 2.
This implies that;
Q = Flow Rate | Darcy’s Law = 14
A = Cross-sectional Area = 4
ΔP = Change in Pressure = 7
L = Length of Pipe = 2
K = Q x L / AΔP
K = 14 x 2 / (4)(7)
K = 28 / 28
K = 1
Therefore, the permeability is 1.
Calculating the Cross-Sectional Area when the Flow Rate, the Permeability, the Change in Pressure and the Length of Pipe is Given.
A = Q x L / KΔP
Where:
A = Cross-sectional Area
Q = Flow Rate | Darcy’s Law
K = Permeability
ΔP = Change in Pressure
L = Length of Pipe
Let’s solve an example;
Find the cross-sectional area when the flow rate is 10, the permeability is 6, the change in pressure is 5 and the length of pipe is 12.
This implies that;
Q = Flow Rate | Darcy’s Law = 10
K = Permeability = 6
ΔP = Change in Pressure = 5
L = Length of Pipe = 12
A = Q x L / KΔP
A = 10 x 12 / (6)(5)
A = 120 / 30
A = 4
Therefore, the cross-sectional area is 4.
Calculating the Change in Pressure when the Flow Rate, the Permeability, the Cross-Sectional Area and the Length of Pipe is Given.
ΔP = Q x L / KA
Where:
ΔP = Change in Pressure
Q = Flow Rate | Darcy’s Law
K = Permeability
A = Cross-sectional Area
L = Length of Pipe
Let’s solve an example;
Find the change in pressure when the flow rate is 24, the permeability is 4, the cross-sectional area is 6 and the length of pipe is 2.
This implies that;
Q = Flow Rate | Darcy’s Law = 24
K = Permeability = 4
A = Cross-sectional Area = 6
L = Length of Pipe = 2
ΔP = Q x L / KA
ΔP = 24 x 2 / (4)(6)
ΔP = 48 / 24
ΔP = 2
Therefore, the change in pressure is 2.
Calculating the Length of Pipe when the Flow Rate, the Permeability, the Cross-Sectional Area and the Change in Pressure is Given.
L = KAΔP / Q
Where:
L = Length of Pipe
Q = Flow Rate | Darcy’s Law
K = Permeability
A = Cross-sectional Area
ΔP = Change in Pressure
Let’s solve an example;
Find the length of pipe when the flow rate is 10, the permeability is 8, the cross-sectional area is 3 and the change in pressure is 5.
This implies that;
Q = Flow Rate | Darcy’s Law = 10
K = Permeability = 8
A = Cross-sectional Area = 3
ΔP = Change in Pressure = 5
L = KAΔP / Q
L = (8)(3)(5) / 10
L = 120 / 10
L = 12
Therefore, the length of pipe is 12.
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the flow rate.
To get the answer and workings of the flow rate 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 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 Materials and Metallurgical under Engineering.
Now, Click on Transport Phenomena under Materials and Metallurgical
Now, Click on Flow Rate under Transport Phenomena
The screenshot below displays the page or activity to enter your values, to get the answer for the flow rate according to the respective parameter which is the Permeability (K), Cross-Sectional Area (A), Change in Pressure (ΔP) and Length of Pipe (L).
Now, enter the values appropriately and accordingly for the parameters as required by the Permeability (K) is 9, Cross-Sectional Area (A) is 12, Change in Pressure (ΔP) is 3 and Length of Pipe (L) is 10.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the flow rate and presents the formula, workings and steps too.