# Different Versions of Poiseuille's Law?

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#### Bah_Gawd_BME

##### New Member
5+ Year Member
In my studying I came across a different version of Poiseuille's Law than I'm used to seeing.

While I am used to seeing it in this form:

I just saw a problem easily solved by using the form below, which is showing a "resistance to flow" value 'R' rather than a flow rate 'Q':

How can one of them include a flow rate yet the other includes resistance, while appearing to be the same equation? Would anybody be able to break this down and explain it to me?

The two forms are the same because the flow rate is equal to the pressure difference divided by the resistance to flow.

Q = flow rate
ΔP = pressure difference
R = resistance to flow

Q = ΔP / R (basic flow equation)

Poiseuille's Law expresses the resistance in terms of the vessel/pipe and flow parameters.

R = (8*η*L) / (π*r^4), where:

η = fluid viscosity (viscosity is a measure expressing resistance to stress)
L = vessel/pipe length