Poiseuille law and friction force help

[notorious]

Homework Statement

Poiseuille's law is valid for fluids with constant speed. So how is this equation used to determine blood flow? If the friction force created is smaller than the pressure difference in the vessel, shouldn't the blood accelerate? Or if the friction force is large, shouldn't the blood speed gradually decrease?

Relevant Equations

Poiseuille

İ dont know

 

[gmax137]

What friction force? The poiseuille flow assumes laminar no slip at the conduit wall. The only "friction" is due to the fluid viscosity.

The Derivation section in the Wikipedia article is pretty clear.

Edit: maybe Chet can help here, calling @Chestermiller

 

[Chestermiller]

The velocity profile for the flow adjusts so that the viscous friction force at the wall is equal to the pressure drop force along the tube.

 

[jbriggs444]

If the friction force created is smaller than the pressure difference in the vessel, shouldn't the blood accelerate? Or if the friction force is large, shouldn't the blood speed gradually decrease?

An equilibrium will be attained.

If the flow rate is low so that the pressure difference dictated by Poiseuille is smaller than the pressure difference applied to the vessel then the flow will indeed accelerate. It will accelerate until it is large enough that the pressure difference dictated by Poiseuille matches the pressure difference applied to the vessel.

If the flow rate is high so that the pressure difference dictated by Poiseuille is larger then the pressure difference applied to the vessel then the flow will indeed decrease. It will decrease until it is small enough that the pressure difference dictated by Poiseuille matches the pressure difference applied to the vessel.

If you know the pressure difference that is applied to the vessel, its length, its radius and the viscosity of the fluid then you can solve the Poiseuille equation for the unknown equilibrium flow rate.

 

[erobz]

Flow problems with blood would be a challenge? Blood is Non-Newtonian - Shear Thinning. I've never tried to do any calculations with it though, so maybe I'm missing boat.

 

[pines-demon]

Flow problems with blood would be a challenge? Blood is Non-Newtonian - Shear Thinning. I've never tried to do any calculations with it though, so maybe I'm missing boat.

It is pretty standard in physics for biology courses to teach all the fluid mechanics as if it applies perfectly to veins.