3.5.3 Experimental principles
Viscosity is a physical quantity to describe the flow resistance of a fluid.The fluid can be a kind of liquid or gas,but the term is normally related to liquids.In principle,liquid viscosity is affected by many factors,such as the size and the shape of the substance,the interactions between them,and its temperature.It is very important to measure the liquid viscosity in modern medicine and industry.For example,the transport of oil in a closed pipeline is affected by its viscosity,especially for a long distance.Therefore,it is a mandatory requirement to measure the viscosity of transmission oil prior to designing the pipeline.In order to measure the liquid viscosity,a number of methods have been proposed,including the falling ball method,rotating tube method,and capillary method.Among them,the falling ball method is a simple and effective approach,which is based on measuring the velocity of a falling ball in a tube filled with the target liquid.In this experiment,the viscosity coefficients of castor oil under different temperatures are determined by the falling ball method.
According to Stokes formula,when a sphere ball drops in an infinite continuous liquid with a small speed,the viscosity resistance(viscosity drag)can be expressed as:
Where r is the radius of the solid sphere,η is the coefficient of liquid viscosity,v is the dropping velocity of the sphere.Therefore,the sphere ball initially accelerates due to the gravity followed by reaching a constant settling velocity(its acceleration becomes to zero)after a brief transient period.In this process,three vertical forces act on the sphere ball,namely the gravity force G the buoyancy force F,and the viscosity drag f,as shown in Figure 3.5.5.The gravity force and buoyancy force can be expressed as follows:
Where ρ is the density of the solid sphere,ρ0 is the density of the fluid,and g is the gravitational acceleration(9.8 m/s2 in this experiment).
When the sphere achieves a steady state during the falling process,the viscous drag and buoyant force of the sphere are balanced by the gravitational force(see Figure 3.5.5),which can be expressed as:
Then:(https://www.daowen.com)
Where d is the diameter of the sphere,v0 is the velocity of the sphere in uniform motion.
However,the glass tube(cylinder-shape)used in this experiment is not infinite vast,Equation(3.5.5)must be revised as:
Figure 3.5.5 Schematic diagram of force analysis
Clearly,the key point in this experiment is to measure the sphere’s terminal velocity,which is usually calculated by measuring the time t the sphere requires to fall a given distance L based on the formula of L=vt.Therefore,substituting this formula into the equation above,it can be expressed as:
As is mentioned before,the viscosity of liquid strongly depends on the nature and temperature of the liquid.In general,the viscosity decreases rapidly as its temperature increases.For example,the viscosity of castor oil changes～10 % when its temperature changes 1℃near the room temperature.Therefore,it is necessary to measure the liquid viscosity at different temperatures.Aiming to accurately measure the viscosity of the liquid,it is important to accurately control its temperature.
