# Buckingham pi fluid mechanics

## 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.

BruceW
Homework Helper
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)

Chestermiller
Mentor

## 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