Properties such as specific weight and density measure the “heaviness” of a fluid. It is highly possible that two liquids with the same specific weight and density have a different flow pattern. This motivates us to find another quantity to describe the “fluidity” of the fluid.
VISCOSITY AND SHEARING STRESS
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SHEARING STRESS ON A DISK
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VIDEO LECTURE
MAIN CONCEPTS
We relate the shearing stress with the rate of change of the shearing strain and get  Get the Printer Friendly VersionCOMMENTS
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LESSON
Let’s think of a hypothetical experiment that sheds some meaning to this property. We place a liquid between two very wide parallel plates. The bottom plate is rigidly fixed but the upper plate is free to move. When the top plate is moved with a force P, the top plate will move continuously with a velocity U as illustrated below.
There has to be a resistance to the movement caused by the “fluidity” of the liquid, roughly speaking. We say that a shearing stress, This shearing stress acts on the plate and by Newton’s third law, it also acts on the liquid, causing it to deform continuously. Upon closer inspection, the upper plate moves with the pate velocity, U, and the fluid in contact with the bottom plate has zero velocity. The fluid between the two plates would move with the velocity govern by the velocity function
Time to introduce some variables. In a small time increment,
Since
At this point
From experimental results, we conclude that the shearing stress,
This result indicates that for common fluids such as water, oil and air the shearing stress and rate of shearing strain (velocity gradient) can be related with the relationship of the form
where the constant of proportionality is designated by the Greek symbol Depending on convention, I usually talk about the shearing stress on the fluid. While there is no strict rule to this, I leave it to the reader to understand the concept of shearing stress and that by Newton’s third law, the shearing stress acting on the fluid and on the plate are equal and opposite and on different bodies. All information presentated, less questions and exercises, is original content of Donny, with slight references to various books.
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is developed at the plate-liquid interface. Our objective is thus to find a mathematical expression for 
.
or if found to vary linearly, 
. We say that a velocity gradient, 
is developed in the fluid between the pates. This gradient may or may not be constant depending on the complexity of the fluid.
, an imaginary vertical line AB in the fluid would rotate through an angle, 
, so that
, it follows that
is a function not only of the force P but also of time. It doesn’t seem reasonable to relate the shearing stress, 
to 
. A way around this is to consider the rate at which 
is changing, and define the rate of shearing strain, 
, as
, increases in direct proportion to the shearing strain, that is
(mu) called the absolute viscosity, dynamic viscosity, or simply the viscosity of the fluid. The actual value of the viscosity depends on the particular fluid, and it should be noted that for a particular fluid, the viscosity is highly depended on the temperature.
