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VISCOSITY Matt Amine Nassim

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Viscosity Viscosity is an internal property of a fluid that offers resistance to flow If the fluid has a high viscosity it strongly resists flow, If the fluid has a low viscosity, it offers less resistance to flow

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**How to measure viscosity**

There are many ways to measure viscosity The falling-sphere method is a simple way to study viscosity fluids at varying temperatures

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**Falling-sphere method**

A cylinder is filled with fluid and two marks placed at the ends of the distance You drop a sphere into a liquid and measure the time required for the sphere to travel a calibrated distance Layers of fluid molecules sliding over other layers with type of frictional forces depending on the viscosity. Fluid stationary at wall moves with increasing velocity away from wall

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THEORY The force needed to separate molecules of the fluid according to Stokes is : F = 6(pi)Rnvc R: radius of the sphere n: viscosity of the fluid vc: velocity of the sphere This force can be set equal to the gravitational force modified to account for the buoyant effect as follows

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**pS : the density of the sphere**

THEORY 6 (pi) R n vc = 4/3 (pi) R3 (pS-pL) g pS : the density of the sphere pL : the density of the liquid g : acceleration due to gravity

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THEORY velocity can be set equal to L/t (distance/time) and the equation solved for n as n = [2 g R2 (pS-pL) t] / 9L

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THEORY The velocity must be modified for the compression of the fluid by the cylinder walls vc = v ( x) x is the ratio of sphere diameter to cylinder diameter

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THEORY The velocity must also be modified for the finite falling distance by vc = v ( y ) y is the ratio of sphere diameter to total liquid height

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THEORY velocity can now be described as vc = v ( x) ( y).

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**n = [2 g R2 (pS-pL) t] / [9L (1 + 2.4x) (1 + 1.65y)].**

THEORY The new values for vc can now be substituted into equation n = [2 g R2 (pS-pL) t] / [9L ( x) ( y)]. Different size particles yield dramatically different settling velocities. all variables necessary to calculate n can be measured directly except for density, which can be easily calculated from measurements [1].

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**Estimated Cost 2m Glass Tube: $10 Plastic Sphere: $0.5**

(we might use more than one sphere with different densities depends on the estimated viscosity of the fluid) Stop Watch: $0

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