# Practical Investigation Into Viscosity

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Introduction

### Practical Investigation Into Viscosity

Aim: To investigate the rate of descent of an object falling through a liquid due to gravity and the factors which affect the viscosity of the liquid.

Theory: Viscosity is the resistance a material has to change in form. This property can be thought of as an internal friction. Something which is very important when investigating viscosity is laminar flow. If a fluid or gas is flowing over a surface, the molecules next to the surface (the ones clinging to the walls) have zero speed. As we get farther away from the surface the speed increases. This difference in speed is a friction in the fluid or gas. It is the friction of molecules being pushed past each other. You can imagine that the amount of clinging-ness between the molecules will be proportional to the friction. This amount of clinging-ness is called viscosity. Thus, viscosity determines the amount of friction, which in turn determines the amount of energy absorbed by the flow.

Viscosity can be determined in the following way: Work is force times distance and it takes energy to do work whilst power is the energy times time. Imagine a school laboratory filled knee deep with oil. On top of the oil is a large plate of metal that we want to slide across the surface to the other side of the room. If you think about the cube of oil under the metal plate resisting the motion we can determine a unit for viscosity:

- Friction is a force (in Newtons) acting along the direction of travel times the distance (in meters) so it is a Nm.
- This frictional force obviously scales with the surface area (in m2) of the top of the cube, which brings us to Nm/m2.
- We move the plate a distance (in meters) so now we have Nm/m3 of work.
- Multiplying by time (in Seconds) to get to power, we end up with Nms/m3 which simplifies to Ns/m2. This is viscosity; a unit of power per unit of area.

Middle

George Stokes' law of viscosity established the science of hydrodynamics. We most often run into him with the work he did on the settling of spheres, but he also derived various flow relationships ranging from wave mechanics to viscous resistance.

Stokes papers on the motion of incompressible fluids, the friction of fluids in motion, and the equilibrium and motion of elastic solids exemplifies his wide range of influence in physics. His works on the transmission of acoustic waves through viscous materials (like tar) are also of interest.

Stokes also investigated the wave theory of light, named and explained the phenomenon of fluorescence, and theorized an explanation of Fraunhofer lines in the solar spectrum. He suggested these were caused by atoms in the outer layers of the Sun absorbing certain wavelengths. However when Kirchhoff later published this explanation Stokes disclaimed any prior discovery.

In short Stokes was an all-around wiz kid (whose name we can pronounce). (If you know of any good stories about George email them here). Stokes came up with a formula that can predict the rate at which a sphere falls through a viscous gas or liquid. He was the first to understand why a mouse can fall 1000 feet and walk away yet a man would be dead.

## Stoke’s great Law of Drag

#### If

r = the radius of a sphere in cm

d1 = the density of the sphere in g/cm3

d2 = the density of the fluid in g/cm3

g = the local gravitational acceleration in cm/S2

c = the Viscosity of the fluid in Poise

v = the terminal velocity in cm/S

#### Then

v = 2r2g(d1-d2)/9c

This velocity is the terminal or ultimate velocity the sphere will attain falling through the liquid or gas in question.

Conclusion

2) The second major factor was the viscosity of the liquid in which the ball bearing descends. The more viscous liquid made the ball bearing descend at a slower rate.

I can also conclude that the temperature of the liquid in which the ball bearing descends through can increase or decrease the rate of descent. With a higher temperature the liquid becomes less viscous and the ball bearing descends at a faster rate.

3) I have found that the angle in which the ball bearing descends through will decrease the speed of when it will reach the bottom. However as I mentioned in the discussion an extra force was acting upon this and therefore made this experiment invalid.

4) The final conclusion to be drawn from my investigation, is that the ball bearings seemed to reach their terminal velocity in the same timed interval. For experiment 1 it was 40-60 cm and for experiment 2 this was also 40-60. Therefore I would be able to conclude with a third liquid that it may be possible that the liquid does not effect the point in which a ball bearing reaches its terminal velocity.

However I can conclude that the size of the ball bearing and also the mass does not effect where it reaches its terminal velocity. As you already know, if two objects of the same size but with different masses are dropped from the same height they will descend and hit the ground at the same time. It is only air resistance that will affect the descent if the objects size is slightly different. I can relate this to my experiments in finding the terminal velocity of the ball bearings through the liquid, and therefore explain why the occurance happened with only a slight varience with the very large ball bearings.

This student written piece of work is one of many that can be found in our GCSE Forces and Motion section.

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