hi my name is Farah Malone and today we're going to be talking about how we can calculate the viscosity of a fluid by dropping a spherical object in it this will involve a quick experiment that requires the following materials a stopwatch a magnet bar a graduated cylinder or the fluid and the steel ball before we can conduct the experiment it's important to place some markings on your graduated cylinder showing the lengths between some of the ticks on it this will be important when calculating the terminal velocity of the ball the experiment is as follows first we're going to be filling the graduated cylinder with our fluid of choice this fluid is of unknown viscosity and the purpose of this experiment is to calculate its viscosity will then drop the spherical ball in it or a steel ball in it it doesn't need to be a steel ball it just needs to be a ball of known density because we'll need its density in the calculations since we're using a steel ball we can use a magnet bar to remove it and we'll repeat this experiment a few times just so that we can be more sure of our results looking at the free body diagram of the sphere at terminal velocity we'll see that there are three forces acting on it in the positive y-direction we have the drag force and the buoyant force and in the negative y-direction we have the gravitational force or you might be familiar with the with the buoyant force and the gravitational force the drag force may be news to some of you so let's quickly talk about how we can derive the equation for the drag force this is derived through Stokes law which says that the drag force depends on the size of the sphere at the terminal velocity and the coefficient of viscosity so the drag force is going to be equal to K which is some constant multiplied by R the radius to the power of a multiplied by the viscosity to the power of being multiplied by the velocity to the power of C to find a B and C we can simply equate the units on the right and left hand sides of this equation and if we do this we're going to find that a equals 1 B equals 1 and C equals 1 if we repeat the experiment that was explained previously knowing all of the variables knowing the viscosity as well will find that K is equal to 6 pi now if we plug this into the equation we forget that the drag force is equal to 6 pi multiplied by the coefficient of viscosity multiplied by the radius of the sphere multiplied by the terminal velocity that it reaches we keep saying terminal velocity what exactly do we mean by this if you did forget let's revisit it quickly the terminal velocity is the speed that the ball is going to reach once it stops accelerating in the fluid so it'll be anything at Point C and Beyond now it's finally time to calculate the viscosity well we know that at terminal velocity the sum of the forces acting on the sphere is going to be equal to zero and the sum forces in the y-direction is the drag force plus the buoyant force minus the gravitational force we already know that the drag force is equal to 6 pi multiplied by the viscosity multiplied by the radius and the terminal velocity and we know that mg minus the buoyant force is equal to 4 over 3 PI R cubed into the density of the ball minus the density of the fluid multiplied by gravity if we use these two equations and plug them into the equation in the first line on this slide we can rearrange to find that the viscosity of the fluid is equal to 2 over 9 R squared into the density of the ball minus the density of fluid times gravity over the terminal velocity now to make this more applicable to the experiment described we can substitute the radius and the velocity out of the equation and find that the coefficient of viscosity is equal to D the diameter squared into the density of ball minus the density of the fluid multiplied by gravity multiplied by the time over 18 times the length now the time here is the time for the ball to travel through the length in the denominator and this is how we were able to find viscosity it's very simple and can be done in almost any laboratory or classroom I hope you enjoyed this quick podcast and if you wish to read more please feel free to this any of the references thank you