1. A –Level Physics: Fluids: Fluid motion + Viscosity

2. a. be able to use the equation for viscous drag (Stokes’s Law)
Objectives:
51.
a. be able to use the equation for viscous drag (Stokes’s Law)
F = 6𝜋ηrv.
b. understand that this equation applies only to small spherical objects moving at low speeds with laminar flow (or in the absence of turbulent flow) and that viscosity is temperature dependent
Additional skills gained:
Application of knowledge to wider contexts

3. Starter: Fermi Question
Try to arrange the densities of the fluids (Highest at the top). Remember fluids can be both liquid or gas!
Water, Ethanol, Carbon Dioxide, Air, Hydrogen, Mercury, Helium
Mercury, water, ethanol, carbon dioxide, air, helium, hyrdrogen

4. Complex Questions
A 500ml flask containing carbon dioxide gas has a mass of g, a pump is then used to remove 80% of the gas. The mass of the flask and gas is now g. Calculate the density of carbon dioxide.
First Q: pg177 in text book. Difference in mass= 0.79g, which in kg is 7.9x10-4. That’s the mass of 80% of the gas, so to work out density d=m/v, and the volume that would have taken up is 80% of 500, so 400 x 10-6 (for m3). M/v= 1.98 (3 sig figs)

5. Complex Questions
Calculate the density of the hot air in a balloon floating at a fixed height close to the ground. The density of the cold air is 1.4kgm-3. The total mass of the balloon’s fabric gondola, fuel, burners and occupants is 700kg and it’s volume is 2500m3
First Q: pg177 in text book. Difference in mass= 0.79g, which in kg is 7.9x10-4. That’s the mass of 80% of the gas, so to work out density d=m/v, and the volume that would have taken up is 80% of 500, so 400 x 10-6 (for m3). M/v= 1.98 (3 sig figs)

6. Moving Liquids
Fluids can be said to move in either laminar flow or turbulent flow.
The movement velocity of a fluid (gas or liquid) can be represented by streamlines, which are arrowed lines showing the path taken by small regions of fluid.
In laminar flow, like slow moving water, adjacent layers do not cross over one another as there is no abrupt changes in speed or direction
However in turbulent flow the fluid swirls around in vortices or eddy currents so streamlines are no longer continuous
Laminar
flow
What is the equation we use to calculate density and include units/symbols
Laminar
flow

7. Visualising Flow
Describe the flow of the gas over these two objects (a) a car (b) a block
Car:
Laminar flow of gas over the top of the car as the streamlines stayed continuous due to gradual change of direction
At back of the car, the streamlines crossed into one another causing turbulent flow.

8. Context 1: How does a plane fly?
You have 5mins as a pair to come up with an idea of HOW a plane gains LIFT. .

9. Draw a neat copy of this diagram, adding labels where appropriate
Flow in context
Draw a neat copy of this diagram, adding labels where appropriate
Below is an image of an aerofoil (i.e. like the wing of a plane), as no aerofoil is perfect, the laminar flow that goes over the wing naturally produces turbulent flow at the end. The better the wing design, the less turbulence it produces!
. Draw a diagram of the second point: the eddy causes some air to circulate around, thus going against the flow underneath but WITH the flow on top, so by vector resolution, this means the velocity of the air above is higher than the velocity below.
The air moving over the aerofoil is faster than the air underneath.
This is because of a circulation of some air around the aerofoil (clockwise).

10. Flow in context
Describe the flow of the gas over these two objects (a) a car (b) a block
As the air moves faster over the top, this means that there is a difference in pressure on the wing. This means that there is more force applied to the bottom of the wing, resulting in uplift (and drag) .

11. Write a small list of factors that would affect flow through a pipe
Context 2: Pipeworks
Write a small list of factors that would affect flow through a pipe
In low speed fluids or high viscosity fluids, flow tends to be laminar through a pipe.
There is a parabolic distribution of velocities with the fastest moving stream in the centre.
If the fluid moves too quickly, eddies can start to form (turbulence)
Speed of flow, radius of the tube, density of the fluid and viscosity of the fluid. Affects the efficiency of fluid transfer so the rate needs to be controlled to not reach critical limit.
Sometimes in the food industry, when molten sugar or chocolate is transferred by pipe, unwanted air bubbles can form. What could have caused this during the flow and how could it be stopped?

12. Viscosity
Viscosity is defined as ‘the magnitude of internal friction within a fluid’ a.k.a ‘how sticky it is’ and as such how resistant it is to flow
Come up with a short list of liquids with high viscosity at the top and low viscosity at the bottom
Rho (kgm-3), 2100kgm-3, temperature

13. Viscosity η F
Greek symbol: Eta
Coefficient of viscosity U
When a sphere moves slowly through a liquid, the relative movement of the liquid around the sphere is laminar
As the molecules its passing through will stick to the surface as it travels, a viscous drag (F) is created
Rho (kgm-3), 2100kgm-3, temperature
This force was shown to be related to the radius of the sphere, the velocity of the sphere and the coefficient of viscosity ( η ) W

14. This relationship is called
Viscosity
Greek symbol: Eta
Coefficient of viscosity
(Nsm-2) η F U
This relationship is called
Stoke’s law
Radius of sphere (m)
Rho (kgm-3), 2100kgm-3, temperature
Velocity of sphere (ms-1)
Drag force (N) W

15. Bernoulli’s Principle
No spin
Spin
Rho (kgm-3), 2100kgm-3, temperature

16. Measuring Viscosity using Stoke’s Law
Read page 181 of the text book and make notes on how to measure viscosity using Stoke’s law
Start reading the literature for your next core practical (Core practical 4) and complete the tasks.

17. a. be able to use the equation for viscous drag (Stokes’s Law)
Objectives:
51.
a. be able to use the equation for viscous drag (Stokes’s Law)
F = 6𝜋ηrv.
b. understand that this equation applies only to small spherical objects moving at low speeds with laminar flow (or in the absence of turbulent flow) and that viscosity is temperature dependent
Additional skills gained:
Application of knowledge to wider contexts
Liquid universe: