Help with Buckingham Pi theory on turbine

In summary: They are equivalent to kg * m / s^2. So T should be kg * m^2 / s^2.In summary, the conversation involves a request for assistance in understanding two dimensionless equations that were created using the Buckingham Pi Theory for a situation with a Reynolds number of 10^5. The equations involve the variables T (torque), p (water density), w (rotation), d (diameter), and u (velocity). The goal is to understand the relationship between rotation and force, but the person has had trouble finding the correct answer using the Buckingham Pi Theory.
  • #1
Valgeirp
1
0
I was wondering if someone is very well into the Buckingham Pi Theory and can assist me in understanding the outcome.
I have two dimensionless equations and I need to get an understanding on how they were made by the Buckingham Pi theory. The situation is considered for the reynolds number 10^5.
The two equations are
upload_2015-9-23_18-18-0.png
and
upload_2015-9-23_18-18-19.png

Where T is N*m force, p water densitykg/m^3, w is (rad/s), d is diamater (m)and u is velocity (m/s). The two variables that we are looking at are the relationship between the rotation (rad/s, w) and Force T (n*m)
Can someone help me understand how these two equations were made I have tried making them with the Buckingham Pi theory. Somehow I never end up with the answer I want.
 
Engineering news on Phys.org
  • #2
Valgeirp said:
I was wondering if someone is very well into the Buckingham Pi Theory and can assist me in understanding the outcome.
I have two dimensionless equations and I need to get an understanding on how they were made by the Buckingham Pi theory. The situation is considered for the reynolds number 10^5.
The two equations are
View attachment 89215 and View attachment 89216
Where T is N*m force, p water densitykg/m^3, w is (rad/s), d is diamater (m)and u is velocity (m/s). The two variables that we are looking at are the relationship between the rotation (rad/s, w) and Force T (n*m)
Can someone help me understand how these two equations were made I have tried making them with the Buckingham Pi theory. Somehow I never end up with the answer I want.
First of all, T is not a force. It is a torque if it has units of N-m.

Second, Newtons (N) are derived units under the SI system.
 

Related to Help with Buckingham Pi theory on turbine

1. What is the Buckingham Pi theory and how does it relate to turbines?

The Buckingham Pi theory is a method used to analyze physical systems and reduce the number of variables involved in the system. It is commonly used in fluid mechanics, including in the study of turbines. The theory helps to identify which variables are important in a particular system and how they are related to each other.

2. How does the Buckingham Pi theory help in understanding turbine performance?

By using the Buckingham Pi theory, researchers can identify the key parameters that affect the performance of a turbine, such as the rotational speed, blade shape, and fluid flow characteristics. This allows for a more in-depth understanding of how these variables impact the efficiency and output of a turbine.

3. Can the Buckingham Pi theory be applied to all types of turbines?

Yes, the Buckingham Pi theory can be applied to all types of turbines, including gas, steam, and hydraulic turbines. However, the specific variables and equations used may vary depending on the type of turbine and the specific research being conducted.

4. How is the Buckingham Pi theory used in the design of turbines?

The Buckingham Pi theory is often used in the design process of turbines to optimize their performance and efficiency. By identifying the key variables and relationships, engineers can make informed decisions about the design and operation of the turbine to achieve the desired output and minimize any potential issues.

5. Are there any limitations to the Buckingham Pi theory when applied to turbines?

Like any scientific theory, there are some limitations to the Buckingham Pi theory when applied to turbines. For example, it may not account for all the complexities and nuances of real-world systems, and there may be some uncertainties in the results. Additionally, the accuracy of the theory depends on the quality of the data and assumptions used.

Similar threads

Buckingham Pi Theory: Propeller & Pipe Flow Analysis for Jay
    • Mechanical Engineering
Replies
1
Views
3K
Rules of choosing repeating variable in Buckingham pi theorem
    • Engineering and Comp Sci Homework Help
Replies
5
Views
9K
Buckingham Pi Theorem Explained: Understanding Variables and Parameters
    • Mechanical Engineering
Replies
1
Views
2K
Buckingham Pi / Dimensional analysis
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
A Problem evaluating an anticommutator in supersymmetric quantum mechanics
    • Quantum Physics
Replies
3
Views
646
Dimension Analysis and buckingham pi
    • Introductory Physics Homework Help
Replies
1
Views
1K
Buckinghams PI-Theorem
    • Introductory Physics Homework Help
Replies
10
Views
2K
Buckingham Pi Theorem: Choosing Common Variables
    • Advanced Physics Homework Help
Replies
1
Views
1K
Help with Inverted Pendulum on Cart EoM
    • Mechanical Engineering
Replies
1
Views
1K
Ts = temperature of steamModel Boiler: Negative Rate of Change of Enthalpy
    • Mechanical Engineering
Replies
17
Views
1K

Hot Threads

Recent Insights

Back
Top