PLEASE HELP in Deriving Terminal Velocity Equation

[hibachii]

PLEASE HELP! in Deriving Terminal Velocity Equation :)

Homework Statement

The terminal velocity of a mass m, moving at 'high speeds' through a fluid of density
ρ(kg m^-3), is given by v = sqrt(2mg/DρA) where A is the cross sectional area of the object (m^2) and D a dimensionless "drag coefficient".

i) Show that equation is dimensionally correct
ii) Estimate the terminal velocity of an Australian $1 coin. Take D to be ~0.3.

Homework Equations

v = sqrt(2mg/DρA)

The Attempt at a Solution

I'm completely stuck. I have no clue as in how to even start. I'm so sorry :(

 

[tiny-tim]

welcome to pf!

hi hibachii! welcome to pf!

(have a square-root: √ and try using the X² tag just above the Reply box )

what are the dimensions of each symbol in √(2mg/DρA)?

check that when you combine them they come to the same as v

 

[JazRad]

I'm going to assume your in the same Physics Class as I am.

If you go to Page 7 of the the book "Physics for Scientists and Engineers" by Serway it explains how to do Dimensional Analysis and that will explain how to do (i).

For (ii) you will need to look up a value for the density of air and then estimate the mass and area of the coin remembering that the coin would be rotating as it fell through the air

 

[hibachii]

Cheers guys. Helped a lot.

P.S Jazrad what class are you in for physics 101?

 

[hibachii]

Hey jazrad thanks but I am still stuck. I've looked at page 7 and 8 but it only shows dimensions for velocity and acceleration. I've still got a lot of unknowns like D, A, m and ρ.
I tried subbing in L/T for v and L/T^2 for g but I am still left stuck. Please give some more help although you have provided me with a very good start.
Cheers

 

[tiny-tim]

hey hibachii!

(try using the X² icon just above the Reply box )

Ive still got a lot of unknowns like D, A, m and ρ.

(D is given as dimensionless )

to find the dimensions of an unfamiliar variable, decde what units it's measured in (m/s² for example), then convert each unit to dimensions (m/s² = L/T²)

start with ρ, the density …

what units is it measured in? ​