Calculating Shear Stress in a Fluid Mechanics Problem

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Discussion Overview

The discussion revolves around calculating shear stress in a fluid mechanics problem involving two cubes connected by a string on an inclined plane covered with oil. Participants explore the forces acting on the cubes, the role of shear stress, and the necessary equations to solve for tension and terminal velocity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant describes a fluid mechanics problem involving cubes on an incline and seeks clarification on calculating shear stress and its effects on the system.
  • Another participant provides a viscosity value and a formula for friction due to shear stress, suggesting a relationship between shear stress and velocity.
  • A participant questions the source of the viscosity value and requests clarification on the shear stress equation and its components.
  • It is noted that the shear stress equation is derived from the definition of shear stress for a Newtonian fluid.
  • Participants discuss the opposition of shear stress to motion, drawing parallels to friction.
  • Definitions of variables in the shear stress equation are provided, including shear stress, viscosity, velocity, and thickness of the fluid layer.

Areas of Agreement / Disagreement

Participants generally agree on the definition and role of shear stress in the context of fluid mechanics, but there are questions regarding specific values and calculations, indicating some uncertainty and a lack of consensus on the viscosity and shear stress equations.

Contextual Notes

There is a reliance on the definitions of viscosity and shear stress, and the discussion includes assumptions about the fluid being Newtonian. Specific values for viscosity and shear stress calculations are not universally accepted, leading to potential variations in the approach.

Who May Find This Useful

Individuals studying fluid mechanics, particularly those interested in the dynamics of forces on inclined surfaces and the effects of viscosity in fluid systems.

Nenad
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I'm working on a fluid mechanics problem and I am not too sure how to approach it. There is a system with an inclined plane and 2 cubes, one attached to the other via a massless string and run through a massless pulley. One cube is dangeling down the vertical edge and the other is on the incline. They both weigh the same amount. The incine is 30 degrees and the question asks to calculate the tension in the string and the terminal velocity of the cubes. The incline is covered with a thin 0.1mm thick layer of oil which has a density of 886kg/m^3 and a dynamic viscosity of 0.29N s/m^2. The information it gives me is that the cubes specific gravity is 2.7 and the side dimentions are 20cm. The oil distribution can be considered to be linear.

I have it set up as a classical mechanics question, but not having any previous experience in fluids, I need to know what kind of force the fluid wil make with the Cube on the incline. I figure that there will be a shear stress. I have No idea how to calculate this. The rest of the problem I know how to set up. Is this shear stress calculated as a constant and then treated like kinetic friction, or is it considered a force? If someone could just quicky give me a quick explanation and an equation or two on how to claculate the force exerted by the fluid, that would be great.

Regards,

Nenad
 
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Viscosity = 256.94 Pas

Friction due to shear stress, F = 102776v

Cube mass, m = 21.6kg

m g (1 - Sin \theta) = 102776v
v = 4.0988ms-1
 
how did you get that viscosity? and the constant for the hear stress equation. If you could please expliain, I would really appreciate it.

Regards,

Nenad
 
You were given the kinematic viscosity, you need the simple viscosity, which is the kinematic viscosity multiplied by the density.

The shear shress equation is based on the definition of shear stress for a Newtonian fluid.
Tau = mu*v/z
 
so shear stress is in opposition to the motion, just like friction right. And could you also ezplain what the vriables are in the shar stress equation. I know the questions I'm asking are simplistic, but I need a definite answer. Thanks in advance.

Regards,

Nenad
 
Shear stress opposes relative motion in the fluid.

Tau = shear stress; mu = viscosity; v = velocity; z = thickness of layer.

Hope this helps.
 
thanks a lot speed. I really appreciate the help.

Regards,

Nenad
 

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