A fluid with a viscosity of 0.1 Pa·s flows through a pipe of radius 0.05 m. What

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Question: A fluid with a viscosity of 0.1 Pa·s flows through a pipe of radius 0.05 m. What is the shear stress if the flow rate is 0.01 m³/s?

Options:

Correct Answer: 0.4 Pa

Solution:

Using the formula for shear stress, τ = (4 * η * Q) / (π * r^3), we find τ = 0.4 Pa.

A fluid with a viscosity of 0.1 Pa·s flows through a pipe of radius 0.05 m. What is the shear stress if the flow rate is 0.01 m³/s?

A fluid with a viscosity of 0.1 Pa·s flows through a pipe of radius 0.05 m. What is the shear stress if the flow rate is 0.01 m³/s?

Step 1: Identify the given values. We have viscosity (η) = 0.1 Pa·s, flow rate (Q) = 0.01 m³/s, and radius (r) = 0.05 m.
Step 2: Write down the formula for shear stress (τ): τ = (4 * η * Q) / (π * r^3).
Step 3: Calculate r^3 (the radius cubed). Since r = 0.05 m, r^3 = 0.05^3 = 0.000125 m³.
Step 4: Substitute the values into the formula. τ = (4 * 0.1 * 0.01) / (π * 0.000125).
Step 5: Calculate the numerator: 4 * 0.1 * 0.01 = 0.004.
Step 6: Calculate the denominator: π * 0.000125 ≈ 0.0003927.
Step 7: Divide the numerator by the denominator: τ = 0.004 / 0.0003927 ≈ 0.4 Pa.
Step 8: Conclude that the shear stress (τ) is 0.4 Pa.

Viscosity – Viscosity is a measure of a fluid's resistance to flow and deformation.
Shear Stress – Shear stress is the force per unit area exerted parallel to the surface of a material.
Flow Rate – Flow rate is the volume of fluid that passes through a given surface per unit time.
Pipe Flow – The behavior of fluid flow through pipes, often analyzed using principles of fluid dynamics.