2 ViscosityViscosity is an internal property of a fluid that offers resistance to flowIf 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 viscosityThe 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 distanceYou drop a sphere into a liquid and measure the time required for the sphere to travel a calibrated distanceLayers 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 THEORYThe force needed to separate molecules of the fluid according to Stokes is :F = 6(pi)RnvcR: radius of the spheren: viscosity of the fluidvc: velocity of the sphereThis 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 THEORY6 (pi) R n vc = 4/3 (pi) R3 (pS-pL) gpS : the density of the spherepL : the density of the liquidg : acceleration due to gravity
7 THEORYvelocity can be set equal to L/t (distance/time) and the equation solved for n asn = [2 g R2 (pS-pL) t] / 9L
8 THEORYThe velocity must be modified for the compression of the fluid by the cylinder wallsvc = v ( x)x is the ratio of sphere diameter to cylinder diameter
9 THEORYThe velocity must also be modified for the finite falling distance byvc = v ( y )y is the ratio of sphere diameter to total liquid height
10 THEORYvelocity can now be described asvc = v ( x) ( y).
11 n = [2 g R2 (pS-pL) t] / [9L (1 + 2.4x) (1 + 1.65y)]. THEORYThe new values for vc can now be substituted into equationn = [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 .
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