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# Viscosity and Poiseuille flow

Understand the concept of viscosity and how it affects the motion of fluids. Learn about the velocity gradient, the role of adhesive forces, and the impact of fluid depth. Discover the units of viscosity and real-life examples of different viscosities. Get introduced to Newtonian and non-Newtonian fluids and the practical application of Poiseuille's Law.

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• viscosity depends on temperature but I don't see temperature anywhere in the formula for viscosity. • difference between density and viscosity please. density to me is how 'thick' something is... i would refer to a 'thicker' liquid as a 'denser' liquid , instead of saying that it is a more 'viscous' liquid. • Nice point.
In scientific language, you need to think of dense as being 'more mass per unit volume'. And that can refer to liquids, solids and gas.
Viscosity, however, only refers to things that flow. Its is a measure of how badly the substance flows.
it would be worth chewing over your thoughts relating now to materials that are viscous but not dense or visa versa....
For example; honey; mercury; glass;
• I don't understand why the flow rate decreases with an increase in L (length of tube). Is the flow slowing down due to the viscous force? • Great question, and I think you're on the right track. Length being inversely proportional to the flow rate describes how there is a cumulative effect of friction the longer a fluid must travel down a pipe because it interacts with longer stretches of material. Therefore, as a fluid increases the distance it moves in contact with a pipe, we expect there to be losses of "forward" motion of its particles, which will register as a loss of flow rate of our incompressible fluid.
• If the fluid depth goes to infinity, the derivation of viscosity implies that zero force would be required to slide the lid over the top of the liquid, which is not reasonable. What's the problem? Are there some hidden assumptions in this derivation? • I think if the depth were really infinity, there would be no friction, because we could perfectly well drag all that water with us. There is no force preventing that because there is no "ocean floor" to provide the friction, and we are assuming there is no other resistance. However, by dragging the water with us we need to conquer its inertia. If the board is 1 kg, the water is 2 kg, and the force pushing the board is 6 N, then acceleration is not 6 N / 1 kg = 6 m/s^2, as is the case when there is no water, but 6 N / (1 kg + 2 kg) = 2 m/s^2, with a = F/m. So the water increases inertia, but doesn't provide a resistance force.

Except with a depth of infinity the mass would probably be infinity too, so it would be impossible to drag the water (a = F/m = F/∞ = 0). But still, you can't blame the mathematics.

Besides, if the board and water are already moving, there sure is no resistance. The "inertial drag" has nothing to do with velocity, only acceleration, and therefore is not viscosity.

It may still be hard to believe there is zero resistance, but even if there was another resistance force, by definition it is not the viscous force, but some other force we had assumed didn't exist.

I like your question too. It really started me thinking.
• Is it safe to assume that A1v1=A2v2=poiseuille law ? • So blood is "thicker" than water because it has a greater viscosity? • How is the viscous force different from the frictional force exerted by the water? If the two are the same, and the coefficient of friction (whether static or kinetic) is independent of both the mass floating above it and the contact surface area, how can the viscous force be dependent on the contact area? • I think they are the same thing. It's just that usually when you're talking about friction (such as air resistance) you don't usually think about layers of fluid but instead simplify the force as proportional to an object's velocity, such as F = k v or F = k v^2.

F = μ N is just an approximation and only applies to dry friction. The force is really caused by quantum phenomena, the electromagnetic force. Basically electrons from different surfaces interact and create resistance. You can't expect a simple equation to describe all instances of that behavior.

I got this off Wikipedia:

Dry friction resists relative lateral motion of two solid surfaces in contact. Dry friction is subdivided into static friction ("stiction") between non-moving surfaces, and kinetic friction between moving surfaces.

Fluid friction describes the friction between layers of a viscous fluid that are moving relative to each other.

Lubricated friction is a case of fluid friction where a lubricant fluid separates two solid surfaces.
Skin friction is a component of drag, the force resisting the motion of a fluid across the surface of a body.

Internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation.

Which shows how naïve we all are--what in the world is skin friction!?
• Well, he said Viscosity depends on the "area of contact" of the lid with the surface of the liquid at . My question is, shouldn't Viscosity also depend on the "material" of the lid ? What if we push lid made of rough material like wood then it may take greater force ! Or, if we take smooth plastic lid, then it may take comparatively lesser force ??
I hope my question is clear !! • your question is clear and very interesting (I like quesitons that make us think)

I am thinking honey or syrup... very viscous..
In my view, if the liquid is 'stuck' to the lid as it flows 'over' the lid then it does not matter what the lid is made of.... stuck is stuck. The material is not sliding on the lid; not slipping. so friction does not play a part beyond 'sticking'  