Stokes' law and falling sphere method

Click For Summary
SUMMARY

The discussion focuses on the application of Stokes' law in determining the viscosity of a fluid using the falling sphere method. Participants emphasize the importance of achieving terminal velocity for accurate viscosity measurements and highlight that transient velocities can skew results. The equation for viscosity, η = 2gr²(d'– d)/9v, is provided, where variables include the radius of the sphere and the densities of the sphere and liquid. It is concluded that the flow around the sphere may not be laminar, which is a critical condition for Stokes' law to apply.

PREREQUISITES
  • Understanding of Stokes' law and its application in fluid dynamics.
  • Familiarity with the concept of terminal velocity and its significance in viscosity calculations.
  • Basic knowledge of ordinary differential equations (ODEs) for analyzing motion.
  • Experience with experimental physics, particularly in measuring fluid properties.
NEXT STEPS
  • Review the derivation and assumptions of Stokes' law in fluid mechanics.
  • Learn how to solve ordinary differential equations related to motion in fluids.
  • Investigate the effects of non-laminar flow on viscosity measurements.
  • Explore methods for ensuring terminal velocity in falling sphere experiments.
USEFUL FOR

Students and researchers in physics, particularly those conducting experiments on fluid viscosity, as well as educators teaching fluid dynamics concepts.

xenoidmaster
Messages
2
Reaction score
0
Homework Statement
I need help at calculating the viscosity of a fluid. I did an experiment of dropping spherical steel balls through a liquid. The diameter includes 5 mm, 10 mm, 15 mm, 20 mm. What makes me confuse is that the viscocity is difference for each diamater, isnt it suppose to be the same? viscocitty shouldnt be affected by diameter of the balls. As i know only terminal velocity will be affected. And so how to calculate the viscocity of the liquid, to get similar answers/small difference between each diameter.
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.
In dire need of help, someone please explain the correct method for this, if its not possible what should i write in the conclusion for this?
 
Physics news on Phys.org
You say you did an experiment. What did you measure? Did you plot your results to see if the viscosity is (or is not) constant?
 
Did you loose your last thread on the topic?

https://www.physicsforums.com/threads/viscosity-by-falling-sphere-equations.1058374/#post-6978437

Your ball is not falling through the liquid (water) at terminal velocity. You have a transient (time varying) velocity to contend with (in your measurements). By solving (with help if necessary) the ODE for position vs time in the other thread you can examine what the data would "look like" if the conditions were actually met in the experiment. It is almost certain (steel ball falling in water) that the flow around the ball is not laminar. This is (likely) an unmet requirement for the equation wish to use.

You need to post the results of the experiments so it can be discussed.
 
Last edited:
Reply
  • Informative
Likes   Reactions: berkeman
xenoidmaster said:
Homework Statement: I need help at calculating the viscosity of a fluid. I did an experiment of dropping spherical steel balls through a liquid. The diameter includes 5 mm, 10 mm, 15 mm, 20 mm. What makes me confuse is that the viscocity is difference for each diamater, isnt it suppose to be the same? viscocitty shouldnt be affected by diameter of the balls. As i know only terminal velocity will be affected. And so how to calculate the viscocity of the liquid, to get similar answers/small difference between each diameter.
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.

In dire need of help, someone please explain the correct method for this, if its not possible what should i write in the conclusion for this?
Let's see your calculations. How far from the walls of the container were the balls?
 

Similar threads

Viscosity by Falling Sphere Equations
  • · Replies 2 ·
Replies
2
Views
2K
Understanding the math of definition of electromotive force
  • · Replies 1 ·
Replies
1
Views
1K
How does the velocity of a ball change without buoyant force acting on it?
  • · Replies 17 ·
Replies
17
Views
2K
Viscosity and temperature, density is changing....
  • · Replies 29 ·
Replies
29
Views
5K
Sanity check on falling steel ball in water
  • · Replies 5 ·
Replies
5
Views
2K
High School Temperature-Dependence of Viscosity of a Fluid?
  • · Replies 1 ·
Replies
1
Views
1K
Why Do Spring Constants Differ Between Hooke's Law and Oscillation Method?
  • · Replies 7 ·
Replies
7
Views
4K
Dynamics of Circular Motion
  • · Replies 12 ·
Replies
12
Views
991
Minimal rotational kinetic energy for a gyroscope to precess
  • · Replies 33 ·
2
Replies
33
Views
3K
Newton's shell theorem - all mass is concentrated at its centre
  • · Replies 16 ·
Replies
16
Views
2K