Dimensional Analysis: Problem & Solution

[abs123456]

Homework Statement

You are performing experiments on a pump and you are interested
in investigating how the working pressure (L1P) and power (P) of the pump vary with
respect to different design conditions. Knowing that in the lab you can manipulate the
volumetric flow (Q), angular velocity of the pump (omega), the diameter of the impeller
(D), the density of the working fluid (p) and the absolute viscosity of the fluid (mu),
find the non-dimensional parameters that are relevant to this problem.

Homework Equations

The Attempt at a Solution

How should i go about doing this problem as i am not sure how to start? Plz help

 

[KataKoniK]

Thank you for your question. it is important to approach problems in a systematic and organized manner. In order to determine the non-dimensional parameters relevant to this problem, you should first start by identifying the variables given in the problem: volumetric flow (Q), angular velocity of the pump (omega), diameter of the impeller (D), density of the working fluid (p), and absolute viscosity of the fluid (mu).

Next, you should consider the units of each variable and try to combine them in a way that removes any units and creates a dimensionless parameter. This can be achieved by using the Buckingham Pi theorem, which states that the number of independent dimensionless parameters needed to describe a problem is equal to the number of variables minus the number of fundamental dimensions (length, mass, time, temperature, etc.).

In this case, you have 6 variables (Q, omega, D, p, mu, and L1P) and 5 fundamental dimensions. This means that there is one dimensionless parameter that can be formed. Without solving the problem for you, I can suggest that you try to combine the variables in a way that creates a dimensionless parameter and see if it is relevant to the problem. If not, try another combination until you find a relevant dimensionless parameter.

I hope this helps you get started on solving this problem. If you have any further questions, please feel free to ask. Good luck with your experiments!