Logical conclusions after playing with physics equations?

[salim271]

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In my spare time (usually during gen chem II which I'm retaking because it didnt transfer to my current uni) I like to doodle MCAT physics equations and play with them along with their units, out of boredom and the fact that its my weakest subject.

So I took the volume flow rate equation for an ideal fluid:

Q = Av
A = pir^2, v = d/t
V (volume) = Ad (in a pipe, so its a cylinder and d is the 'height')
So then Q = V/t?

something similar with the mass flow rate...

I = pQ (p being the density)
If Q = V/t, then I = m/V times V/t, volumes cancel and I = m/t.

Is doing stuff like this alright for the MCAT? If units check, does that mean that its always true? I remember reading somewhere on here that it wasnt always true, but I cant remember the post :/. I think it was one of the 30+ study strategies...

Math, equations and all that stuff is not my strong suit, so any tips other than 'do problems and do practice passages' would be helpful, I already know to do those two .

 

[MD Odyssey]

If units check, does that mean that its always true?

It's not always true, but it often helpful. Dimensional analysis is very powerful, particularly if you know the general form. For example, if you wanted to derive an expression for the period of a pendulum, you could start by gathering all the different variables you think would be included. Obviously, the acceleration due to gravity would be present, as would length. If you neglect air resistance and ignore the mass of the pendulum, you can derive an expression for the period of the pendulum.

If you do this, you'll see that it looks like the square root of the length divided by the acceleration due to gravity. But, all you've really found is what it's proportional to, so we insert a constant somewhere. For an ideal pendulum, that constant of proportionality winds up being 2 pi.

So to answer your question - no, it's not always true. As another example, consider finding the energy stored on a parallel plate capacitor. You might be able to get the variables all worked out using dimensional analysis, but there is no way you would know that there was a factor of 1/2 in the beginning.

However, all that said, it's still a highly useful skill to be able to estimate things or derive an equation using the units.