Rotating Disk ViscometerRotating Disk Viscometer

Problem 1.55

Jillann Walker12.12.06

AbstractAbstract

Given the rotating disk viscometer, determine the viscosity of the oil, and also determine the overall uncertainty in viscosity if each parameter ( M, R, h, f) is +/- 1percent.

DiagramDiagram

Known ValuesKnown Values

• R = 5cm

• h = 1mm

• f = 900rpm

• τ = 0.537 Nm

Solve ForSolve For

• V = Tangential Velocity

-Used in viscosity formula

• μ = Viscosity

AssumptionsAssumptions

• Closed system

• Density is not relevant

• Shear stress is consistent throughout

• Velocity is linear

EquationsEquations

• Viscosity

• Tangential Velocity

hv

v Note: V = Tangential Velocity

v f 2 r rNote: r = radius of disk

SolutionSolution

900rpm

60sec

r

s

m

s

=

2 x 3.14 x 0.05m x 15 = 4.71239

15r

s

hv

v

v f 2 r r

0.537Nm 0.001m( )

4.71239kg

ms 1.14 x 10-4

ExplanationExplanation• Shear takes place at the surface of the disk over the area.

• Higher velocity require lower viscosity

• Higher clearance requires higher viscosity

• 1 percent uncertainty– Largest uncertainty range at 1 on the top and -1 on the bottom of the plate– This is not a 2% difference

Biomedical RelationBiomedical Relation

• Shoulder joint or ankle joint.

• Refer to a ball and socket– The joint fitting will contain liquid of some sort and

depending on the resistance needed to rotate the joint, will determine the viscosity of the liquid.

Questions?Questions?