Question

The following is Poiseuille’s equation which describes the flow of

fluid through a cylindrical tube. The constants are: P is pressure difference1

,

[P] = ML−1T

−2

, r is radius, η is viscosity of the fluid, [η] = ML−1T

−1

, and l

is the length of the tube:

flow rate = πP r4

8ηl

Here is another version of the same equation, where ρ is the density of the fluid,

[ρ] = ML−3

,

flow rate = πρP r4

8ηl

Use dimensional analysis to determine the dimension(s) of the flow rate- Are

these equations the same?

Answer 1

$$[Q_1]=\frac{ML^{-1}T^{-2}L^4}{LML^{-1}T^{-1}}=L^{3}T^{-1}$$

$$[Q_2]=\frac{ML^{-1}T^{-2}L^4ML^{-3}}{LML^{-1}T^{-1}}=MT^{-1}$$

These equations are not the same.