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Which of the following equations represents the relationship between shear stres

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Question: Which of the following equations represents the relationship between shear stress and shear rate in a Newtonian fluid?

Options:

  1. τ = μ(du/dy)
  2. τ = ρg
  3. F = ma
  4. P = F/A

Correct Answer: τ = μ(du/dy)

Solution: 

In a Newtonian fluid, shear stress (τ) is directly proportional to the shear rate (du/dy) with the proportionality constant being the dynamic viscosity (μ).

Which of the following equations represents the relationship between shear stres

Practice Questions

Q1
Which of the following equations represents the relationship between shear stress and shear rate in a Newtonian fluid?
  1. τ = μ(du/dy)
  2. τ = ρg
  3. F = ma
  4. P = F/A

Questions & Step-by-Step Solutions

Which of the following equations represents the relationship between shear stress and shear rate in a Newtonian fluid?
Correct Answer: τ = μ (du/dy)
  • Step 1: Understand what a Newtonian fluid is. A Newtonian fluid is a type of fluid that has a constant viscosity, meaning it flows the same way regardless of the shear rate.
  • Step 2: Know the terms involved. Shear stress (τ) is the force per unit area that causes the fluid to flow, and shear rate (du/dy) is the rate at which the fluid layers move past each other.
  • Step 3: Recognize the relationship. In a Newtonian fluid, the shear stress is directly proportional to the shear rate.
  • Step 4: Identify the proportionality constant. The constant that relates shear stress and shear rate in a Newtonian fluid is called dynamic viscosity (μ).
  • Step 5: Write the equation. The relationship can be expressed as τ = μ * (du/dy), where τ is shear stress, μ is dynamic viscosity, and (du/dy) is shear rate.
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