## Sunday, November 24, 2019

### How does the viscosity of a liquid affect the flow of a sphere through it Essays

How does the viscosity of a liquid affect the flow of a sphere through it Essays How does the viscosity of a liquid affect the flow of a sphere through it Essay How does the viscosity of a liquid affect the flow of a sphere through it Essay The resistance offered by a liquid/fluid (gases and liquids) on a moving object inside it is called viscosity. The flow of liquid occurs as the movement of layers at different speeds which in turn lead to a gradient of speeds and friction among them respectively.Stokes LawThe viscous force offered by a fluid on a ball is directly proportional to the radius of the ball and its speed at a given instant.F is proportional to rF is proportional to vF is proportional to rvK=6= coefficient of viscosityF= 6 ? ? r vF=Frictional Force?= coefficient of viscosityR=Radius of the SphereV=Velocity of the Sphere? =F/6?rv = N/mms-1 =Nm-2s =Pa sI believe that the density of the liquid will be directly proportional to the time taken for the sphere to drop.Viscosity of various fluidsFluidViscosity (Pa s)Hydrogen8.410-6Air17.410-6Xenon2.1210-5(Room temperature)Blood3x10-3Castor oil0.985Glycerol1.5Mercury1.510-3Water8.9410-4Up thrust (U)When an object is fully or partially immersed in a fluid, the fluid exerts a force on the object upwards.Archimedes PrincipleThe up thrust acting on an object that is partially or fully immersed in a fluid, is equal to the weight of the displaced liquid.Up thrust= the upward force on the object.According to Archimedes Principle,Up thrust= Weight of the displaced liquid.= Mass of the displaced liquid x g= Volume of the displaced liquid x density of liquid x gU= v p gU= Up thrustV= VolumeP=DensityG=Gravity on kgm3-1The motion of a sphere inside a viscous liquidWhen a sphere is moving inside a liquid, three forces are acting on it:Weight downwards,Up thrust and Viscous Force upwards.Since F= 6 ? ? r v, the viscous force is increasing with the speed.Since F is increasing, at some point the sum of U and F is going to be equal to W.At this point the resultant force on the sphere is zero, therefore, according to F=MA, a=0, that means the sphere moves at constant speed. This is called the Terminal Velocity.When the sphere is moving at terminal velocity, W= U+F.?= 2r2 g (d-p)/9vtD=density of the sphereP=density of the liquidThe density of the sphere and pulp must be calculated separately using the formula:Density=Mass /VolumeTo find vt, the speed of the sphere must be measured during few intervals to make sure it has reached the terminal velocity.Then the experiment can be repeated to study the change in viscosity with the concentration of the pulp.AimTo find the time taken for a sphere to fall through several viscous liquids and liquids with different concentrations of viscosity.Diagram/EquipmentMethodI filled up the cylinder container with the viscous liquid, which is wallpaper paste (mixed together beforehand).I then placed the sphere on the surface of the liquid.When I let go of the sphere I started the timer.When the sphere reached the bottom, I stopped the timer.Using a ruler I measured the distance travelled.Using Distance / Time I got the speed of the sphere, and the terminal velocity at each 10cm interva l.I then repeated the experiment.PreliminaryIn my preliminary experiment, I tested out different sphere sizes and also the maximum and minimum concentrations of the viscous solutions, so I would know which quantities would be best to use.The diameter of the sphere I chose was 1.3cm, as it was small enough to travel at a constant rate through the liquid.The minimum concentration contained 8g of wallpaper paste in 600ml of water, as it was just viscous enough to take a reading. The maximum was 26g of paste, because after that the sphere doesnt move at all.Results = First ExperimentInterval (cm)Water (ml)Density (kgml-1)Time 1 (Sec)Time 2 (Sec)Time 3 (Sec)Average Time (Sec)1020Total5000.9744s104s146s44s105s145s45s102s146s145.6s1020Total5100.9518396618406717386666.3s1020Total5200.9413355812351.0014335858.6s1020Total5300.9361624717248162424.0s1020Total5400.914101551115491414.6s1020Total5500.9038133713481313.0s1020Total5600.8937103710461110.3s1020Total5700.882572583677.3s1020Total5800.872 462562445.3s1020Total5900.861241241233.7s17g PasteChanging Water from 500ml upwardsResults = Second ExperimentPaste (g)Density (kgml-1)Time 1 (Sec)Time 2 (Sec)Time 3 (Sec)Average Time (Sec)80.970.410.370.380.38100.960.370.340.430.38120.960.440.500.500.48140.950.630.680.650.65160.951.281.501.281.35180.944.185.416.535.37600ml WaterChanging Paste from 8g upwardsThe graph for the first experiment shows that as Density increases, so does time, though they are not directly proportional because they dont go up in equal amounts. There is also an anomaly, which could have been caused by human or systematic error.For the second experiment the graph is quite different. This shows that as Density increases, time actually decreases. So the two quantities are inversely related. There is a constant pattern at first, but then due to human and systematic error there are a few anomalies.Evaluation/ConclusionYou can see from the first graph that density and time are directly proportional, so as one go es up so does the other. This shows that the relationship between density and time is valid.For the second graph, the two quantities are inversely related. This is because for that one the liquid is getting more viscous, so slowing down the sphere.To improve the experiment I could take better precautions to reduce the errors, especially the human errors as they can be prevented more easily.I could have tried to find out my reaction time and eliminate that from the time to make it more accurate.Some of the limitations are that you cant use very big objects, because they wont fit through the cylinder, and also different shapes, because they have sides of different areas.