Viscosity by Falling Sphere Equations

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In summary, the "Viscosity by Falling Sphere Equations" refers to a set of mathematical relationships used to determine the viscosity of a fluid by analyzing the motion of a sphere falling through it. The key principle is based on Stokes' law, which describes the drag force experienced by a small spherical object in a viscous medium. By measuring the terminal velocity of the falling sphere and applying relevant equations, one can calculate the fluid's viscosity, taking into account factors such as sphere radius, fluid density, and gravitational acceleration. This method is particularly useful in laboratory settings for characterizing various fluids.
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Homework Statement
I have recently conducted an experiment to measure the viscosity of some liquids using the falling sphere method and a high-speed camera. I used different diameters of sphere starting from 2.5, 5, 10, 15 and 20 mm. What I want to prove using stokes law equation is that diameter of sphere doesn't affect viscosity of a liquid and it will stay the same. I guess it's okay if it has a little bit different viscosity for each diameter, however when I calculate using the stokes law formula, the difference is so big and when I compared it to the real viscosity of the liquid it's also so different. The liquid is water, which was supposed to have 0.001 Pas, but my calculated value is around 0.84 Pas. I need help, does diameter affect viscosity? if I'm not wrong it only affects the terminal velocity. How please??
Relevant Equations
η = 2gr^2(d'– d)/9v
where:
v is the particles' terminal velocity velocity (m/s),
r is the radius of the sphere,
g is the gravitational acceleration,
d' is the density of the falling sphere,
d is the density of the liquid,
and η is the viscosity.
I have recently conducted an experiment to measure the viscosity of some liquids using the falling sphere method and a high-speed camera. I used different diameters of sphere starting from 2.5, 5, 10, 15 and 20 mm. What I want to prove using stokes law equation is that diameter of sphere doesn't affect viscosity of a liquid and it will stay the same. I guess it's okay if it has a little bit different viscosity for each diameter, however when I calculate using the stokes law formula, the difference is so big and when I compared it to the real viscosity of the liquid it's also so different. The liquid is water, which was supposed to have 0.001 Pas, but my calculated value is around 0.84 Pas. I need help, does diameter affect viscosity? if I'm not wrong it only affects the terminal velocity. How please??
 
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xenoidmaster said:
Homework Statement: I have recently conducted an experiment to measure the viscosity of some liquids using the falling sphere method and a high-speed camera. I used different diameters of sphere starting from 2.5, 5, 10, 15 and 20 mm. What I want to prove using stokes law equation is that diameter of sphere doesn't affect viscosity of a liquid and it will stay the same. I guess it's okay if it has a little bit different viscosity for each diameter, however when I calculate using the stokes law formula, the difference is so big and when I compared it to the real viscosity of the liquid it's also so different. The liquid is water, which was supposed to have 0.001 Pas, but my calculated value is around 0.84 Pas. I need help, does diameter affect viscosity? if I'm not wrong it only affects the terminal velocity. How please??
Relevant Equations: η = 2gr^2(d'– d)/9v
where:
v is the particles' terminal velocity velocity (m/s),
r is the radius of the sphere,
g is the gravitational acceleration,
d' is the density of the falling sphere,
d is the density of the liquid,
and η is the viscosity.

I have recently conducted an experiment to measure the viscosity of some liquids using the falling sphere method and a high-speed camera. I used different diameters of sphere starting from 2.5, 5, 10, 15 and 20 mm. What I want to prove using stokes law equation is that diameter of sphere doesn't affect viscosity of a liquid and it will stay the same. I guess it's okay if it has a little bit different viscosity for each diameter, however when I calculate using the stokes law formula, the difference is so big and when I compared it to the real viscosity of the liquid it's also so different. The liquid is water, which was supposed to have 0.001 Pas, but my calculated value is around 0.84 Pas. I need help, does diameter affect viscosity? if I'm not wrong it only affects the terminal velocity. How please??
What's the Reynolds number for the sphere falling in water? Stokes law is valid for laminar flow.

i.e. Does the velocity of the sphere as it falls match expectations for the equation of motion:

$$ m\dot v = mg - \beta v $$

Where ##\beta## is approximately constant?
 
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Just to check, please post one set of values of all the measurements, quoting units.
 
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FAQ: Viscosity by Falling Sphere Equations

What is the basic principle behind the viscosity measurement using the falling sphere method?

The basic principle involves measuring the terminal velocity of a sphere as it falls through a fluid. The viscosity of the fluid is then calculated using Stokes' Law, which relates the drag force on the sphere to its velocity, radius, and the fluid's viscosity.

How is Stokes' Law applied in the falling sphere method to determine viscosity?

Stokes' Law states that the drag force on a sphere moving through a viscous fluid is proportional to the sphere's radius, the fluid's viscosity, and the sphere's velocity. By measuring the terminal velocity of the sphere, we can rearrange Stokes' Law to solve for the fluid's viscosity.

What are the limitations of using the falling sphere method for viscosity measurement?

The falling sphere method is most accurate for low Reynolds numbers, where the flow around the sphere is laminar. It is less accurate for high-viscosity fluids or very small or very large spheres, as these conditions can lead to deviations from the assumptions of Stokes' Law.

Why is it important to ensure the sphere reaches terminal velocity in the falling sphere method?

Terminal velocity is the constant speed that the sphere reaches when the gravitational force pulling it down is balanced by the drag force and buoyant force acting upward. Accurate viscosity measurements depend on the sphere reaching this steady state, as Stokes' Law is derived under these conditions.

How do temperature variations affect the viscosity measurement using the falling sphere method?

Viscosity is highly temperature-dependent; typically, fluids become less viscous at higher temperatures. Accurate viscosity measurements require controlling and knowing the temperature of the fluid, as variations can lead to significant errors in the calculated viscosity.

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