Resistance in Fluid Systems Mr. Andracke Principles of Technology

Viscosity Fdrag =  x Av/ y Viscosity has the units of (pressure) (time). The SI units for viscosity are Pa x s Fdrag =  x Av/ y

Stokes’ Law Irishmen George Stokes used viscosity and the equations of fluid flow to predict the drag force on a sphere moving through a fluid. Stokes’ Law applies to objects moving at low enough speeds that the flow of fluid is streamlined or laminar.

Stokes’ Law Fdrag = 6rv 6 =Constant for sphere R = Radius of object V = Speed of object  = Fluids Viscosity

Stokes’ Law Fdrag = 6rv Example:

Poiseuille’s Law Poiseuille was a physician, who experimented with flowing water, and learned that the rate at which fluid flows through a tube increases proportionately to the pressure applied the fourth power of the radius of the tube. Poiseuille’s Law gives the volume flow rate of a fluid flowing through a tube or pipe.

3 Factors of Resistance In fluid flow resistance decreases the flow rate though a pipe. Poiseuille’s Law shows how this resistance depends on three factors: Dependence on Radius Dependence on Length Dependence on Viscosity

Dependence on Radius The larger the radius of a pipe, the greater volume of fluid per second Fluid resistance decreases as pipe radius and cross-sectional area increase.

Dependence on Length Longer pipes have higher fluid resistance Volume flow rate is inversely proportional to length

Dependence on Viscosity Abrupt changes in the direction of fluid flow can cause turbulence and increase resistance Fluid resistance increases as viscosity increases.

Poiseuille’s Law V = -  r4 8 L R = Radius of Pipe or Tube  = P2 – P1 = Viscosity L = Length of Pipe or Tube

Poiseuille’s Law V = -  r4  8 L Example:

Poiseuille’s Law Help with Poiseuille's Law http://hyperphysics.phy-astr.gsu.edu/hbase/ppois.html

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