Poiseuille law and friction force help

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Homework Help Overview

The discussion revolves around the application of Poiseuille's law in the context of fluid flow, particularly focusing on the friction forces involved in laminar flow through a conduit, such as blood flow in vessels.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between friction forces and pressure differences in fluid flow, questioning how these forces affect acceleration and equilibrium in the system. Some discuss the implications of blood being a non-Newtonian fluid and the challenges this presents in calculations.

Discussion Status

The discussion is active, with participants raising questions about the dynamics of flow and friction forces. Some have provided insights into the equilibrium conditions that arise from the interplay of pressure and friction, while others are considering the complexities introduced by the non-Newtonian nature of blood.

Contextual Notes

There is mention of specific parameters such as pressure difference, vessel length, radius, and fluid viscosity, which are relevant to applying Poiseuille's equation. The discussion also reflects on the assumptions made in standard physics teachings regarding fluid mechanics in biological contexts.

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?
Relevant Equations
Poiseuille
İ dont know
 
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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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