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In 1851, George Gabriel Stokes derived an expression, now known as Stokes' law, for the frictional force - also called drag force - exerted on spherical objects with very small Reynolds numbers (e.g., very small particles) in a continuous viscous fluid. Stokes' law is derived by solving the Stokes flow limit for small Reynolds numbers of the generally unsolvable Navier-Stokes equations: : where: : :* Fd is the frictional force (in N), :* μ is the fluid's dynamic viscosity (in Pa s), :* Ris the radius of the spherical object (in m), and :* V is the particle's velocity (in m/s). If the particles are falling in the viscous fluid by their own weight due to gravity, then a terminal velocity, also known as the settling velocity, is reached when this frictional force combined with the buoyant force exactly balance the gravitational force. The resulting settling velocity (or terminal velocity) is given by: : where: : :* Vs is the particles' settling velocity (m/s) (vertically downwards if ρp > ρf, upwards if ρp < ρf ), :* g is the gravitational acceleration (m/s2), :* ρp is the mass density of the particles (kg/m3), and :* ρf is the mass density of the fluid (kg/m3). Note that for molecules Stokes' law is used to define their Stokes radius.

Stokes's law is the basis of the falling-sphere viscometer, in which the fluid is stationary in a vertical glass tube. A sphere of known size and density is allowed to descend through the liquid. If correctly selected, it reaches terminal velocity, which can be measured by the time it takes to pass two marks on the tube. Electronic sensing can be used for opaque fluids. Knowing the terminal velocity, the size and density of the sphere, and the density of the liquid, Stokes' law can be used to calculate the viscosity of the fluid. A series of steel ball bearings of different diameter is normally used in the classic experiment to improve the accuracy of the calculation. The school experiment uses glycerine as the fluid, and the technique is used industrially to check the viscosity of fluids used in processes. It includes many different oils, and polymer liquids such as solutions. The same theory can be used to explain why small water droplets (or ice crystals) can remain suspended in air (as clouds) until they grow to a critical size and start falling as rain (or snow and hail). Similar use of the equation can be made in the settlement of fine particles in water or other fluids. The CGS unit of kinematic viscosity was named "stokes" after his work.

Measurement Laboratory No. 3

EGR 101

7

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Í

Í

È

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Á

Ë

Ê

-

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+

-

=

5

3

95

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09

.2

104

.2

1

D

d

D

d

D

d

c

m

m

where m

c

is the corrected viscosity, and D is the internal diameter of the cylinder.

5) Using Stokes Law determine the viscosity of the unknown fluid by using the

average velocities of each of the two different size spheres.

7. Concluding Questions

1) In Part I, Step 8, what is the value of the Reynold's Number, and using this value is

Stokes' Law valid? Why, or why not?

2) In Part II, Step 4, were there any difficulties in measuring the fall times of the brass

spheres? Would increasing the diameter of the brass sphere make the problem

worse or better?

3) In Part III, Step 4, how did your predicted fall times compare to measured fall

times? What were the possible sources of error if any that occurred?

4) Given your calculated density and viscosity of your unknown fluid in Part IV,

confirm your findings with the lab TA to identify your unknown fluid. Who did

your results compare to the data from the TA?

5) In the lab manual there is a formula listed for Stokes Law that contains a correction

factor relating the diameter of the sphere and the diameter of the graduated

cylinder. Measure the diameter of the graduated cylinder and determine the

corrected fall times for the two different size spheres in Part IV?

6) Was there a significant difference between the corrected values for fall times and

the non-corrected values? How much did the diameter of the graduated cylinder

influence the fall time of the sphere?

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What would happen if you have 2 liquids with different densities in the same container?

The liquid with higher density will settle at the bottom, while the one with lower density will float on top due to the principle of buoyancy. The liquids will not mix and will form distinct layers based on their densities.


How do you tell which one is the densest liquid if you pour three liquids into a beaker?

To identify a liquid that is most dense it would be at the bottom of a container because the the most dense sinks while the least dense float at the top. example. if your teacher gave you an experiment to do and she gave you olive oil,dish soap,and color water. and you put those liquid in a see through container the least dense is the alcohol because that has the least density in it, and the most dense is soap. so if you put a couple of liquids in a container the most dense will appear at the bottom while the least will be on top. hope this help:)


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Can you describe the density changes between the two substances that a lava lamp contains?

The lava lamp contains two substances: the lava (wax) and the liquid (usually a type of oil). The lava is denser than the liquid when cold, causing it to sink to the bottom of the lamp. When the lamp is turned on and the wax heats up, it becomes less dense than the liquid, causing it to rise to the top. This continuous cycle of heating and cooling creates the lava lamp's mesmerizing motion.

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What would happen if you have 2 liquids with different densities in the same container?

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Can a solid be more dense than a liquid?

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