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Buckingham pi fluid mechanics

  • #1

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.
 

Answers and Replies

  • #2
BruceW
Homework Helper
3,611
119
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)
 
  • #3
19,954
4,108

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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