Falling Sphere Viscometer

Introduction

A Falling Sphere Viscometer is a device used to measure the viscosity of a fluid. This method of viscosity measurement involves observing the time it takes for a sphere of known size and density to descend through a stationary fluid of unknown viscosity. The speed of descent is directly related to the viscosity of the fluid. This method is based on the principles of Stokes' Law, which predicts the sphere's settling velocity.

Principle

The principle of the Falling Sphere Viscometer is based on Stokes' Law, which states that the drag force on a small sphere moving through a viscous medium is proportional to the velocity of the sphere. The law assumes that the motion of the sphere is steady and that the Reynolds number is small. The latter condition implies that the flow around the sphere is laminar and the drag force is linearly related to the velocity.

Design and Operation

A typical Falling Sphere Viscometer consists of a tall, narrow, vertical glass tube filled with the test fluid. The sphere, often made of steel or glass, is dropped into the tube, and the time it takes for the sphere to fall a certain distance is measured. The tube is typically graduated to allow for easy measurement of the fall distance. The sphere must be denser than the fluid so that it will sink rather than float.

A tall, narrow, vertical glass tube filled with a clear fluid. A small sphere is being dropped into the tube.

The sphere's descent is timed between two marks on the tube. The viscosity of the fluid can then be calculated using the known properties of the sphere and the measured fall time. The sphere's diameter, density, and fall time are all factors in the calculation of viscosity.

Calculations

The viscosity of the fluid (η) can be calculated using the following equation derived from Stokes' Law:

η = (2/9) * (ρ_s - ρ_f) * g * d^2 / v

where: ρ_s is the density of the sphere, ρ_f is the density of the fluid, g is the acceleration due to gravity, d is the diameter of the sphere, and v is the velocity of the sphere (calculated as the fall distance divided by the fall time).

Limitations and Considerations

While the Falling Sphere Viscometer is a simple and effective method for measuring viscosity, it does have certain limitations. It is most accurate for fluids with low viscosities, as high viscosity fluids can cause the sphere to descend too slowly for accurate measurement. Additionally, the method assumes that the fluid is Newtonian, meaning its viscosity is constant at different shear rates. Non-Newtonian fluids, whose viscosity changes with shear rate, may not yield accurate results with this method.

The size and density of the sphere are also important considerations. The sphere must be small enough to minimize turbulence but large enough to be easily observed. Its density must be greater than that of the fluid, but not so great that it falls too quickly for accurate timing.

Applications

Falling Sphere Viscometers are used in a variety of industries to measure the viscosity of fluids. In the petroleum industry, they are used to test the viscosity of oil, while in the food industry, they may be used to test the viscosity of liquids like honey or syrup. They are also used in the pharmaceutical industry to test the viscosity of various drugs and solutions.