Shear Stress due to Laminar flow

Calculate the gradient dv/dy and the shear stress will be tau = -eta*dv/dy.In summary, the shear stress exerted by the oil on the wall of the pipe is 106.7 Pa, calculated using the average velocity gradient. However, the correct answer is 213 Pa, which can be found by considering the non-uniform velocity distribution across the pipe. A polynomial velocity function of degree 2 can be used to calculate the gradient at the pipe wall, resulting in the correct value for shear stress.
  • #1
ice87
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Homework Statement


Oil of Density 888kg/m^3 and viscosity 0.8Pa*s is flowing in a horizontal pipe of diameter 0.15m. The local flow velocity at the centerline is 10m/s. find the shear stress exerted by the oil on the wall of the pipe.


Homework Equations


tau = -eta*(dv/dy)


The Attempt at a Solution


= -0.8*(10/0.075) = 106.7 Pa
but the given solution is 213Pa, exactly twice my answer, what am I doing wrong? thanks
 
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  • #3
As AlephZero stated, you should find a velocity function v(y) as a polynomial of degree 2 satisfying the given velocity condition in the middle streamline.
 

1. What is shear stress due to laminar flow?

Shear stress due to laminar flow is the force per unit area that is exerted on a surface by a fluid in motion. This type of stress occurs when a fluid flows in parallel layers, or lamina, with no mixing between the layers.

2. How is shear stress calculated?

Shear stress is calculated using the formula τ = μ(dv/dy), where τ represents shear stress, μ is the dynamic viscosity of the fluid, and dv/dy is the velocity gradient in the direction perpendicular to the flow.

3. What factors affect shear stress due to laminar flow?

The factors that affect shear stress due to laminar flow include the viscosity of the fluid, the velocity of the fluid, and the distance between the layers of fluid. The type of surface the fluid is flowing over can also affect shear stress.

4. How is shear stress different from normal stress?

Shear stress is a type of stress that occurs parallel to a surface, while normal stress occurs perpendicular to a surface. Shear stress is caused by forces that are applied parallel to the surface, while normal stress is caused by forces that are applied perpendicular to the surface.

5. What are some real-world applications of shear stress due to laminar flow?

Shear stress due to laminar flow is an important concept in the design of pipelines, blood flow in the human body, and aerodynamics in aircraft. It is also used in the manufacturing of various products, such as paints and coatings, to ensure proper application and adhesion to surfaces.

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