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**Resistance in Fluid Systems**

Mr. Andracke Principles of Technology

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**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

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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.

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**Stokes’ Law Fdrag = 6rv 6 =Constant for sphere R = Radius of object**

V = Speed of object = Fluids Viscosity

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Stokes’ Law Fdrag = 6rv Example:

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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.

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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

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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.

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**Dependence on Length Longer pipes have higher fluid resistance**

Volume flow rate is inversely proportional to length

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**Dependence on Viscosity**

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

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**Poiseuille’s Law V = - r4 8 L R = Radius of Pipe or Tube**

= P2 – P1 = Viscosity L = Length of Pipe or Tube

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Poiseuille’s Law V = - r4 8 L Example:

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**Poiseuille’s Law Help with Poiseuille's Law**

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**Complete the Math Lab Activity & Receive Handout for Tomorrows Lesson**

Any Questions?? Complete the Math Lab Activity & Receive Handout for Tomorrows Lesson

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