Assertion (A): In the boundary layer concept, the shear stress at theouter edge of the layer is considered to be zero.
Reason (R): Local velocity is almost equal to velocity in potential flow.
a)
Both A and R are true and R is the correct explanation of A
b)
Both A and R are true but R is NOT the correct explanation of A
c)
A is true but R is false
d)
A is false but R is true
Correct answer is option 'A'. Can you explain this answer?

Question

Assertion (A): In the boundary layer concept, the shear stress at theouter edge of the layer is considered to be zero.
Reason (R): Local velocity is almost equal to velocity in potential flow.

a)
Both A and R are true and R is the correct explanation of A
b)
Both A and R are true but R is NOT the correct explanation of A
c)
A is true but R is false
d)
A is false but R is true

Correct answer is option 'A'. Can you explain this answer?

Answer

Boundary Layer Concept and Shear Stress

Boundary layer concept is an important concept in fluid mechanics, which describes the thin layer of fluid that develops near a solid surface where the fluid velocity is zero. The concept is used to determine the velocity distribution, shear stress, and drag force on a solid surface. In this context, the given assertion and reason can be explained as follows:

Assertion (A): In the boundary layer concept, the shear stress at the outer edge of the layer is considered to be zero.

This assertion is true. The boundary layer is a thin region of fluid where the velocity gradient is significant. In this layer, the fluid velocity increases from zero at the surface to the free stream velocity at the outer edge of the layer. Due to the viscosity of the fluid, the velocity gradient produces a shear stress at the surface, which is responsible for the drag force on the solid surface. However, as the fluid moves away from the surface, the velocity gradient decreases, and the shear stress also decreases until it becomes zero at the outer edge of the layer. Therefore, the shear stress at the outer edge of the boundary layer is considered to be zero.

Reason (R): Local velocity is almost equal to velocity in potential flow.

This reason is also true. Potential flow is a theoretical concept that assumes the fluid to be inviscid and incompressible. In such a flow, the velocity distribution is determined by the potential function, which satisfies the Laplace equation. The potential flow is an idealized flow, which neglects the effects of viscosity and turbulence. However, in the boundary layer, the velocity is strongly influenced by viscosity and turbulence, which cause the velocity to deviate from the potential flow. Nevertheless, as the fluid moves away from the surface, the velocity tends to approach the free stream velocity, which is close to the velocity in potential flow. Therefore, the local velocity in the boundary layer is almost equal to the velocity in potential flow.

Conclusion

Both the assertion and reason are true, and the reason is the correct explanation of the assertion. The shear stress at the outer edge of the boundary layer is zero, because the velocity gradient decreases to zero. The local velocity in the boundary layer is almost equal to the velocity in potential flow, because the fluid tends to approach the free stream velocity.

Answer

Potential flow means flow outside the boundary layer means treated as free stream flow velocity(U-infinity) where shear is zero  which we already know

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