Torque lost using Newton's law of viscosity

Then use the given information to plug in values and solve for the torque lost in this situation. In summary, the problem asks to calculate the torque lost when two circular plates with known parameters slide over each other, with a linear speed profile in the lubricant between them. Using Newton's law of viscosity, the torque can be calculated by finding the angular velocity and using the derivative of the radius with respect to z.
  • #1
felipe de carli
1
0

Homework Statement



Two circular plates, as indicated in the figure, slide one over the other. Calculate the torque lost in this situation. The rotation w of the internal radius of the plates R1, the outer radius of the plates R2, the absolute viscosity of the lubricant between the plates (η) and the thickness of the lubricant film (e) are known. The speed profile is linear in the lubricant.

n0jtZJc.png


Homework Equations



Newton's law of viscosity:
τ = η ∂u / ∂z

The Attempt at a Solution



My first attempt was to get the angular velocity w from the formula v = ω R.
Substituting in the formula, I get τ = η w ∂R / ∂z.
I am stuck in here. How can I derive ∂R / ∂z ? I mean, this derivative should be equal 0, because they are not dependent. Is my approach correct?
Thank you in advance
 

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  • #2
$$\frac{\partial u}{\partial z}=\frac{\omega R}{e}$$
 
  • #3
felipe de carli said:
The rotation w of the internal radius
Some text missing in there?

I would start by finding u as a function of r and z.
 

FAQ: Torque lost using Newton's law of viscosity

What is Newton's law of viscosity?

Newton's law of viscosity states that the shear stress of a fluid is proportional to the velocity gradient of the fluid. In other words, it describes how the viscosity of a fluid affects its flow under an applied force.

How is torque lost calculated using Newton's law of viscosity?

To calculate torque lost using Newton's law of viscosity, you need to know the viscosity of the fluid, the surface area of the object in contact with the fluid, and the relative velocity between the fluid and the object. The formula for torque lost is τ = ηAω, where τ is the torque lost, η is the viscosity of the fluid, A is the surface area, and ω is the relative velocity.

What factors affect torque lost in a fluid using Newton's law of viscosity?

The factors that affect torque lost in a fluid include the viscosity of the fluid, the surface area of the object in contact with the fluid, and the relative velocity between the fluid and the object. Additionally, the temperature and pressure of the fluid can also affect its viscosity and therefore impact the torque lost.

Can Newton's law of viscosity be applied to all types of fluids?

Newton's law of viscosity can be applied to most common fluids, such as water, oil, and air. However, it may not accurately describe the behavior of non-Newtonian fluids, which have a variable viscosity depending on the applied force or shear rate.

How does torque lost affect the flow of a fluid?

Torque lost can affect the flow of a fluid by causing it to resist movement or change direction, as well as by dissipating energy in the form of heat. This can impact the efficiency of fluid systems, such as in pumps and turbines, and can also lead to increased wear and tear on mechanical components.

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