Which of the following equations represents the relationship between shear stress and shear rate in a Newtonian fluid?
Practice Questions
1 question
Q1
Which of the following equations represents the relationship between shear stress and shear rate in a Newtonian fluid?
τ = μ(du/dy)
τ = ρg
F = ma
P = F/A
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).
Questions & Step-by-step Solutions
1 item
Q
Q: Which of the following equations represents the relationship between shear stress and shear rate in a Newtonian fluid?
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).
Steps: 5
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.
