Viscosity of liquid for falling sphere viscometer

[Dennydont]

Homework Statement

A falling sphere viscometer measures the viscosity of a liquid from the terminal velocity of a tiny, falling sphere. One such device determines that a tiny sphere of radius 46 μm falls through a liquid with a terminal velocity of 2.5 mm/s. If the density of the sphere is 4171 kg/m3 and the density of the liquid is 718 kg/m3 what is the shear viscosity of the liquid?
r sphere = 46 μm
ρ sphere = 4171 kg/m^3
ρ liquid = 718 kg/m^3
v = 2.5 mm/s

Homework Equations

F = 6πηrv
Continuity: ρAv

The Attempt at a Solution

Would I be able to find the Force by using the equation: F = ρAv² which is just the continuity equation times velocity?

 

[Chestermiller]

Homework Statement

A falling sphere viscometer measures the viscosity of a liquid from the terminal velocity of a tiny, falling sphere. One such device determines that a tiny sphere of radius 46 μm falls through a liquid with a terminal velocity of 2.5 mm/s. If the density of the sphere is 4171 kg/m3 and the density of the liquid is 718 kg/m3 what is the shear viscosity of the liquid?
r sphere = 46 μm
ρ sphere = 4171 kg/m^3
ρ liquid = 718 kg/m^3
v = 2.5 mm/s

Homework Equations

F = 6πηrv
Continuity: ρAv

The Attempt at a Solution

Would I be able to find the Force by using the equation: F = ρAv² which is just the continuity equation times velocity?

No. Have you drawn a free body diagram of the sphere, and identified all the forces acting on the sphere? Based on this, have you written out the force balance equation on the sphere?

Chet

 

[brainpushups]

I haven't crunched the numbers but first, unless you are sure which drag term dominates (viscous or inertial), I would first start by evaluating the Reynolds number. My guess is that the viscous term is dominant and you can simply use Newton's second law with the force

F = 6πηrv

set equal to the sphere's weight (the buoyant force is probably negligible).

 

[Chestermiller]

I haven't crunched the numbers but first, unless you are sure which drag term dominates (viscous or inertial), I would first start by evaluating the Reynolds number. My guess is that the viscous term is dominant and you can simply use Newton's second law with the force

It looks like he was instructed to use the creeping flow (viscous flow) equation. That is the equation he has listed under relevant equations.

set equal to the sphere's weight (the buoyant force is probably negligible).

The buoyant force is small but not negligible. Compare the densities in the problem formulation.

Chet

 

[brainpushups]

The buoyant force is small but not negligible. Compare the densities in the problem formulation.

Yes I suppose that an order of magnitude difference is certainly not negligible for the buoyant force in this case.

 

[Dennydont]

It looks like he was instructed to use the creeping flow (viscous flow) equation. That is the equation he has listed under relevant equations.

The buoyant force is small but not negligible. Compare the densities in the problem formulation.

Chet

I used the buoyancy force equation F = ρgV where V is volume, g is gravity and ρ is the density of the sphere. Set it equal to F = 6πηrv and calculated the viscosity there. This is incorrect, and I realize now that I also need to work the density of the liquid into this equation some way. How would I go about doing this?

 

[Chestermiller]

I used the buoyancy force equation F = ρgV where V is volume, g is gravity and ρ is the density of the sphere. Set it equal to F = 6πηrv and calculated the viscosity there. This is incorrect, and I realize now that I also need to work the density of the liquid into this equation some way. How would I go about doing this?

See post #2. Please list the forces acting on the sphere.

Chet