VISCOSITY Matt Amine Nassim

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

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

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 

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

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

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

THEORY The velocity must be modified for the compression of the fluid by the cylinder walls vc = v (1 + 2.4x) x is the ratio of sphere diameter to cylinder diameter

THEORY The velocity must also be modified for the finite falling distance by vc = v (1 + 1.65y ) y is the ratio of sphere diameter to total liquid height

THEORY velocity can now be described as vc = v (1 + 2.4x) (1 + 1.65y).

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 (1 + 2.4x) (1 + 1.65y)]. 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].

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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