Dimension Analysis: Solving x=ut- y^{2} * z^{2} / V

[Philip Wong]

Homework Statement

x=ut- y^{2} * z^{2} / V
x,y,z is length
u is speed
t is time
V is volume

The Attempt at a Solution

m = m/s * s - (m^{2} * m^{2} / m^{3})
m=m- m^{4}/m^{3}
m=m-m
m=0

there is inconsistent? is this correct?

 

[lurflurf]

They are consistent. m-m->m
We do not know if
ut- y^{2} * z^{2} / V
is 0, but even if it is it is 0m.

 

[Philip Wong]

They are consistent. m-m->m
We do not know if
ut- y^{2} * z^{2} / V
is 0, but even if it is it is 0m.

oh right! I was thinking that it was consistent at first, but i have doubt it. So I said it's inconsistent. Now you've explained it I've fully understand it.

So is it alright to assume, a model is consistent when:
no dimension is left unchecked (i.e. appears on both sides of the model), even though both sides doesn't seems to be balanced (e.g. m = m)?

for example:
using the same assumption as my question,
V = (-x^{2} * u) / t

m^{3} = m^{2}s^{-1} * ms^{-2}

m^{3} = m^{3}s^{-3}

therefore is inconsistent because time does not appears on the left hand side?

 

[lurflurf]

That is right.

 

[Philip Wong]

thanks for your help!