Poiseuille law and friction force help

AI Thread Summary
The discussion centers on the relationship between friction force and Poiseuille flow, which assumes laminar conditions with no slip at the conduit wall, where friction is attributed solely to fluid viscosity. It highlights that the velocity profile adjusts to balance viscous friction at the wall with the pressure drop force along the tube. If the friction force is less than the applied pressure difference, blood will accelerate, while a larger friction force will cause a decrease in speed until equilibrium is reached. The Poiseuille equation can be used to determine the equilibrium flow rate based on known parameters like pressure difference, vessel length, radius, and fluid viscosity. Challenges arise in applying these principles to blood flow due to its non-Newtonian, shear-thinning properties.
notorious
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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?
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Poiseuille
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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
 
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.
 
notorious said:
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.
 
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.
 
erobz said:
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.
 

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