Viscosity and density of fluids are the properties that determine the motion through pipelines and biological ducts, which is the main object of hydrodynamics. Laboratory experiments about the density and viscosity measurements are essential in any subject of engineering and biotechnology concerning hydrodynamic topics.
Viscosity is an important parameter for analytical research and process engineering covering the range 10-4 – 1012 Pa•s. There are several methods for measuring the viscosity of a fluid depending on the applied physical law:
a)Newton's equation of the viscosity definition, as the shear strain rate response of a fluid to an applied shear stress.
b)The Stokes equation of motion of a sphere in a liquid, which friction force is proportional to its diameter, velocity and the viscosity of the liquid.
c)The Hagen - Poiseuille equation, which relates the loss of energy in a tube with its length, its diameter, the viscosity and the flow.
This work presents an automated laboratory system to measure the viscosity of a Newtonian fluid which density is known (previously and independently measured). The fluid is water and the used method is the Hagen - Poiseuille equation applied to the flow through a capillary tube in which length and diameter are known. A cylindrical tank filled with water and a capillary tube are required. The tank is drained through the tube by siphon effect. The free surface height of tank water (z) diminishes exponentially over time (t): , where A is a constant and B is a known function of the liquid properties (density and viscosity) and of the tube dimensions (length an diameter).
In order to automate the measurement of the free surface height of water, two fixed metallic electrodes are placed in the tank. An alternating current of 1 kHz frequency is applied and the electrical admittance is measured, which is a function of height (z). Voltage and current intensity are measured with two multimeters communicated with a computer via USB connector. Comparing the admittance measurement as z-function and the developed exponential model, the constant B and the viscosity value are obtained.
The result is a simple and inexpensive setup for student experiment. Furthermore it allows the measuring of an important physical property of liquids, it uses several physical laws such as Hagen - Poiseuille and Bernoulli ones and it applies the practical siphon effect to drain a tank. A theoretical model is carried out which matches the experimental results very well, concepts such as electrical admittance of a liquid between two electrodes. Electrical instrumentation techniques are introduced and the automation of measurements by means of a computer is performed.
The aim of this work is got successfully by a useful laboratory experiment with wide knowledge of different activities and several topics of physics.