Flow Rate Ratio of Two Tubes: Calculation

[Ekh]

Homework Statement

Two tubes carry the same incompressible fluid with viscosity 1.5 Pl. They have lengths L1 = 6 and L2 = 22 m and diameters d1 = 1.2 and d2 = 4.5 cm. What is the ratio of their flow rates F1/F2?

Homework Equations

Poiseuille's law: 8nLI/(pi*r^4)
while n is viscosity
L is the length
R is radius

The Attempt at a Solution

F1= (8*1.5*6*I) / (pi*(1.2/2)^4)
F2= (8*1.5*22*I) / (pi*(4.5/2)^4)

The ratio F1/F2 is:
(8*1.5*6*I) / (pi*(1.2/2)^4)* (pi*(4.5/2)^4)/ (8*1.5*22*I)

F1/F2= 46.296*1.1649= 53.932.

And this is wrong, can u help??

 

[ideasrule]

You need to write out your steps more clearly. 8nLI/(pi*r^4) is not Poiseuille's equation; Poiseuille equation is ΔP=8nLI/(pi*r^4), where I represents flow rate. You now have 2 equations:

ΔP₁=8nLI₁/(pi*r₁^4)
ΔP₂=8nLI₂/(pi*r₂^4)

If you assume the two ΔP's are the same and divide one equation by the other, you'll see your mistake.

 

[Ekh]

Thank you a lot :)