- #1

Plebert

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It's a first year university physics assignment that I'm having a bit of trouble with, any help will be rewarded with kind words!(bit of an empty gift, but it's all I have)

Ok, here's the problem.

The terminal velocity of a mass m, moving at ‘high speeds’ through a fluid of density ρ (kg m^3), is given by

V(terminal)=√((2mg)/(DρA))

where A is the cross-sectional area of the object (m2) and D is a dimensionless “drag coefficient”.

Show that equation is dimensionally correct.

Now, not really being certain what the question is asking for regards 'dimensions' hasn't helped but! I did make an attempt by substituting each variable with it's corresponding units.

e.g.

2mg= 2((m/s^2)x(kg))=((m x kg)/ s^2)and ρA=((Kg/m^3)x(m^2))=Kg x m^(-1)

which yields V(ter)=√((mKg)/ s^2)/mKg

=√(s^2) x D

=s x D

This seems more or less nonsensical.

I'm sure it's probably mathematical error or just a failure to grasp the concept of proving an equations dimensions.

Am I wrong?

what is going on?