How to Determine Pi Groups for Fluid Flow Through an Orifice

AI Thread Summary
The discussion focuses on determining Pi groups for fluid flow through an orifice in a tank. The participant has identified three Pi groups but is struggling to select the appropriate repeating variables for their analysis. They have expressed their understanding of the dimensional units involved, such as fluid density and viscosity. Another participant encourages sharing more details of their work to provide better assistance. The conversation highlights the importance of correctly identifying repeating variables in dimensional analysis for fluid dynamics.
Capablecactus
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Homework Statement


a) A orifice, diameter d (m), in the walls of a tank discharges water under a head, h (m), subjected to gravitational acceleration, g (m/s2). If the fluid has density, ρ (kg/m3)and viscosity, μ (Ns/m2), show that the quantity of fluid Q (m3/s) flowing out of the tank may be expressed by the equation.

Homework Equations


Q= h^2 √gh ϕ( μ/(ρ√g h^(3/2) ) ,h/d)[/B]

The Attempt at a Solution


I've been struggling on this for over a week. I've worked out there's 3 Pi group and i have all the units in dimensional format eg ρ= M/L^3

I can't seem to work out which repeating variables to use, when ot which pi group.Any help or pointers with this would be very much appreciated as i know how to do the next stages.
 
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hi, welcome to physicsforums :)
yeah, you're right, there are 3 Pi groups. So, what does their equation show?
Maybe it is easier to look at it like Q/(h^2 √gh) = ϕ( μ/(ρ√g h^(3/2) ) ,h/d)
 
Capablecactus said:

Homework Statement


a) A orifice, diameter d (m), in the walls of a tank discharges water under a head, h (m), subjected to gravitational acceleration, g (m/s2). If the fluid has density, ρ (kg/m3)and viscosity, μ (Ns/m2), show that the quantity of fluid Q (m3/s) flowing out of the tank may be expressed by the equation.

Homework Equations


Q= h^2 √gh ϕ( μ/(ρ√g h^(3/2) ) ,h/d)[/B]

The Attempt at a Solution


I've been struggling on this for over a week. I've worked out there's 3 Pi group and i have all the units in dimensional format eg ρ= M/L^3

I can't seem to work out which repeating variables to use, when ot which pi group.Any help or pointers with this would be very much appreciated as i know how to do the next stages.
It's hard to help unless you show us what you did.

Chet
 
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