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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where m
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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?
Bottom, think of how a rock sinks to the bottom of water.
It has more density then water.
Bottom.
the less dense liquid will float to the top and the more dense liquid will drift to the bottom
If its less it floats on the surface of the liquid. If its more it will sink to the bottom.
The tendency of a less dense substance to float in a more dense liquid is called buoyancy. Acids are substances that form hydronium ions when dissolved in water.
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:)
Ice water is more dense than warm water.
one liquid would be more dense (bottom liquid) and one would be less dense (top liquid) as oil would go on top of water no matter what unless shaken because oil is less dense than water as water has a density of 1
The liquid which is less dense will float on top of the liquid which is more dense. Density affects the liquid's level.
The more dense liquid will be on the bottom in this case the one that is 1.3
the less dense liquid will float to the top and the more dense liquid will drift to the bottom
solid will be settling at the bottom because liquid can not be denser than solid due to their arrangements of their molecules.
Liquid magma is more dense than the solid material around it.
Water is most dense at +4 Celsius. This is why lakes do not freeze to the bottom at winter. Solid ice is less dense than water.
Condenser use to condense the liquid for e.g: seperation of an emulsion by condensing the liquid & form different layer of oil & water &more dense liquid willlie at the bottom by that we can seperate the liquid. ;-)
If its less it floats on the surface of the liquid. If its more it will sink to the bottom.
Ice cubes are less dense than liquid water, which is why they float.
yes liquid water is more dense than ice water
Liquid water is more dense than ICE , and More dense than water vapour(steam). Liquid water is at its most dense at 2 oC. Water on freezing to ice expands by about 10% of its volume. This is because of the lattice arrangement of water molecules in ice., which does not occur in liquid water., Hence ice floats on water. (icebergs).