1. VISCOSITY
Matt
Amine
Nassim

2. 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

3. 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

4. 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 

5. 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

6. 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

7. 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

8. 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

9. 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

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

11. 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].

12. 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

13. Thank you
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