![]() ![]() For gases and non-polymeric liquids like water, viscosity is independent of the fluid ’s shear stress and history. Other examples are liquid plastics and mud. Fluids that behave in this manner are called non-Newtonian fluids. After paint is applied, only the slow and steady pull of its weight causes it to flow at this slow shear rate the viscosity of paint is high and it resists the tendency to flow or sag. When brushed on (sheared) quickly, fluids such as paint have a low viscosity and flow easily. In general, viscosity is a function of temperature and pressure however, in some fluids viscosity is dependent on the rate of shear and time. ![]() Thick fluids such as tar or honey have a high viscosity thin fluids such as water or alcohol have a low viscosity. The proportionality factor between the shear stress and the velocity difference between the plates is defined as the coefficient of viscosity or simply the viscosity of the fluid. The shear stress is proportional to the speed of the plate and inversely proportional to the distance between the plates. Those fluids that have no resistance to shear stress are called ideal fluids. The applied shear stress keeps the plate in motion and, when the plate velocity is steady, this shear stress is in equilibrium with the frictional and drag forces within the fluid.Īll fluids, except superfluids (those with a complete absence of viscosity), contain some factor that pose a resistance to shear stress. ![]() The applied force per unit area of the plate is called the shear stress. Imagine a fluid between two flat plates one plate is stationary and the other is being moved by a force at a constant velocity parallel to the first plate. Thus, it can be described as a measure of fluid friction. It is commonly described as a resistance to pouring of a liquid, such as the viscosity different grades of automobile oil. ![]() This must be why my text Transport Phenomena by Bird, Stewart, and Lightfoot says the gap must be "small".The viscosity of a fluid is an internal measure of its resistance to continuous deformation caused by sliding or shearing forces. Taken to the extreme, at very large $Y$, $F$ is zero. I just can't imagine myself exerting a smaller force on a doubled gap system. Why should doubling the plate gap cause the force to be halved everything else being equal? Conceptually, I get that the velocity gradient is half what it was and that this is what causes the force to be half but my intuitive picture is lacking. I can't quite understand this one intuitively. Finally it is inversely proportional to $Y$, the plate gap. It is proportional to $V$ which make sense since moving the plate at a higher velocity will require more force. It is proportional to $\mu$ which really is the definition of viscosity (higher viscosity fluid requires more force). It is proportional to $A$ which makes sense as a bigger plate will require more force to move due to the viscous contact with the liquid. One finds that the velocity gradient with respect to distance along $Y$ is linear with velocity at the top plate zero and the velocity at the bottom plate $V$ (no-slip condition). The gap between plates is $Y$ and the flow is presumed/constrained to be laminar. Once steady-state is reached, $F$ and $V$ are constant. Apply a force $F$ parallel to the bottom plate so as to start moving the bottom plate at a speed of $V$. Take the prototypical definition/model of viscosity: Imagine two very large plates separated by a constant small distance with a fluid sandwiched inside. I know $\tau_$ but I am looking for an intuitive picture of the specific question below. I am puzzled by an artifact of the definition of viscosity and need an intuitive picture to help explain it. ![]()
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