Torque and viscosity relations, fluid mechanics

In summary, to find the torque required to rotate one disc relative to the other in the given scenario, we use the definition of viscosity and integrate in the radial direction. Since the oil is very thin, we can assume laminar flow and proceed with the calculations. The final answer is 2.24 Nm.
  • #1
abs123456
15
1
A uniform film of oil 0.13 mm thick separates two circular discs, each 150 mm diameter and
mounted coaxially. Find the torque required to rotate one disc relative to the other at a steady speed
of 400 rev/min if the oil has a viscosity of 0.14 Pa.s. (Ignore edge effects at the rim of the disc).

Answer: 2.24 Nm.

Please could you show me the stages of how to go about getting that answer.
I am getting a bit confused with the variables
 
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  • #2
Use the definition of viscosity then integrate in the radial direction.
The oil is very thin so assume laminar flow; should be straightforward after this
 

What is torque?

Torque is a measure of the twisting force that causes an object to rotate. In fluid mechanics, it is often used to describe the forces acting on a rotating object, such as a propeller or a turbine.

What is viscosity?

Viscosity is a measure of a fluid's resistance to flow. It is a property that describes how easily a fluid can be deformed or sheared. High viscosity fluids, such as honey, are thick and resistant to flow, while low viscosity fluids, such as water, are thin and flow easily.

How are torque and viscosity related?

The relationship between torque and viscosity is described by the equation τ = μΔω, where τ is the torque, μ is the viscosity, and Δω is the change in angular velocity. This equation shows that the torque required to rotate an object is directly proportional to the fluid's viscosity.

How does viscosity affect fluid flow?

The viscosity of a fluid has a significant impact on its flow behavior. High viscosity fluids flow more slowly and have a greater resistance to flow, while low viscosity fluids flow more quickly and have less resistance. Viscosity also affects the formation of boundary layers and the flow patterns of fluids around objects.

What factors affect the torque and viscosity of a fluid?

The torque and viscosity of a fluid are influenced by a variety of factors, including temperature, pressure, and the composition of the fluid. In general, as temperature increases, viscosity decreases, and as pressure increases, viscosity increases. The type and size of particles suspended in a fluid can also affect its viscosity. Additionally, the shape and size of the container or object in which the fluid is contained can impact the torque required to move the fluid.

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