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A –Level Physics: Fluids: Fluid motion + Viscosity 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 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 Complex Questions A 500ml flask containing carbon dioxide gas has a mass of 180.39g, a pump is then used to remove 80% of the gas. The mass of the flask and gas is now 179.60g. Calculate the density of carbon dioxide. 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 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 Laminar one another as there is flow no abrupt changes in speed or direction Laminar flow However in turbulent flow the fluid swirls around in vortices or eddy currents so streamlines are no longer continuous 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. 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. 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! 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). 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) https://www.youtube.com/watch?v=aFO4PBolwFg 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. 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? 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) 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 Viscosity η Greek symbol: Eta F 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 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 Viscosity η Greek symbol: Eta Coefficient of viscosity (Nsm-2) F U This relationship is called Stoke’s law Radius of sphere (m) Drag force (N) Velocity of sphere (ms-1) W Bernoulli’s Principle No spin Spin 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. 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