Hence very small drops of rain and the minute droplets from an aerosol fall slowly through the air. This also shows us that the terminal velocity of a falling sphere in a fluid depends on the square of its radiu s. We also get one equation of terminal velocity in terms of density of falling object and density of the fluid from equation (3): Viscosity η = 2( ρ s – ρ f) gr 2 / (9 v) …………… (3) Terminal velocity equation W = weight of sphere = ms g = Vρ s g = (4/3)πr 3 ρ s g U= weight of displaced fluid = m f g = Vρ f g = (4/3) πr 3 ρ f g This equation gives us the formula of viscosity.įor a sphere of volume V, radius r and density ρ s falling through a fluid of density ρ f and viscosity η with a terminal velocity v, we get the following equilibrium equation: In other words, when terminal velocity is reached we can use the equilibrium equation in this way: upthrust + viscous drag = weight. Derive formula of Viscosity using Stokes’ formula & terminal velocityīy measuring the terminal velocity of a sphere falling through a fluid it is possible to determine the coefficient of viscosity of the fluid. The resultant force then becomes zero, and the sphere continues to fall at a constant velocity known as the terminal velocity. As the velocity of the sphere increases, the viscous drag increases according to Stokes’ law until ( U + F) = W. Initially, a resultant force, R = W – ( U + F) will make the sphere accelerate downward. When a sphere is released and allowed to fall freely in a fluid, it is subjected to three forces: its weight, W, the upthrust, U, and the viscous drag, F.
Now we derive a different equation of viscosity or coefficient of viscosity in terms of terminal velocity. We have already derived one expression of viscosity using the flow of a viscous fluid between two parallel plates. Sutherland’s formula for calculating the viscosity of a gas at a specified gas temperature is shown below along with an explanation of the parameters in the equation. Here we will derive the formula of viscosity using Stoke’s law. Background for Sutherland Formula Viscosity Calculator Excel Spreadsheet.
0 kommentar(er)
