Lab Partners: Laina Maines & Heidi Osterman
Date of Lab: 2/21/11
Due Date: 2/28/11
The goal of this experiment was to determine the viscosity of given liquids. Two different methods were employed, the first measures time of flow of several methanol-water solutions, from point A to point B. The second method involves dropping a foreign object, in this case a sphere, into a cylinder of glycerol and measuring the time it takes for it to travel a specific distance down the tube. The viscosity of a 0%, 20%, 40%, 60%, 80% and 100% methanol by volume solutions was measured to be 0.89, 1.28, 1.53, 1.46, 1.11 and 0.54±0.001P, respectively. The falling sphere method was performed under two different temperatures. At 5.7°C the viscosity of glycerol was calculated to be 29.8±0.1P and at 22.7°C it was 6.3±0.1P.
Viscosity is a property of liquids that measures a fluid’s resistance to flow. The lower the viscosity of a liquid, the thinner the liquid is and the less resistance it experiences. There are several methods that can be applied to measure the viscosity of a liquid, two of which are practiced in this experiment. The first part of the experiment uses an Ostwald viscometer to determine how long it takes a liquid to flow through the capillary tube of the viscometer. Poiseuille’s law demonstrates that the laminar flow of a liquid through a small tube is proportional to the fourth power of the tube’s radius, which is employed in the first method. Poiseuille’s law is given in equation 1, in which dV/dt is the volume flow rate, r is the radius, L is length of the tube, ΔP is the pressure difference across the ends of the tube and η is the viscosity.
After integrating and rearranging equation 1, a simpler equation is obtained for viscosity which is given by equation 2, in which t is the length of time for a liquid of volume V, to flow through a capillary tube of length L and radius r.
The parameters r, V, and L remain constant for a given viscometer and thus all of the constants can be combined to give a cell constant, B, for the viscometer. Since pressure is proportional to the density ρ, of the liquid, equation 2 can be simplified even further to give equation 3.
In order to properly use equation 3, the viscometer must be calibrated and B must be found. This is done so by measuring the time of flow of a liquid of known viscosity and density, in this case pure water. This method for determining viscosity of a liquid is more useful for less viscous substances.
For fluids that are thicker; more viscous, a different method is used more effectively. This alternative method involves measuring the rate of drop of spheres in a specific fluid. When the sphere is dropped, it has an initial acceleration due to gravity. However at some point, an equilibrium state is reached when the buoyant force and drag force balance out the gravitational force. At this point, the sum of the forces is zero and the ball is traveling at a constant velocity called the terminal velocity. Stoke’s law represents this behavior of a small sphere falling through a cylindrical tube filled with a viscous liquid. His law is shown in equation 4 in which g is the acceleration due to gravity, t is the time required for the sphere of radius r to drop a distance L, and ρs and ρL are densities of the sphere and fluid respectively.
Equation 4 is modified to account for “end” and “wall” effects which are caused by the finite dimensions of the cylinder. This modified form of equation 4 is given in equation 5, in which x is the ratio of the diameter of the sphere to...