Bernoulli's equation is not applied within boudary layer because
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The Bernoulli Equation can be considered to be a statement of the conservation of energy principle appropriate for flowing fluids. The qualitative behavior that is usually labeled with the term "Bernoullieffect" is the lowering of fluid pressure in regions where the flow velocity is increased.
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The development of boundary layer in a pipe flow can be explained from the diagram above. As you see, there are two regions in which the flow can be divided. The first portion is the entry length where viscous effects dominate. The thickness of the boundary layer increases till it reaches the centerline and a fully developed velocity profile is said to be formed.
Assuming that the flow is Newtonian, the wall shear stress at any instant of time is given by

To answer your question: During the initial stages of the flow, the thickness of the boundary layer is small and wall shear stress is the highest due to rapidly changing gradients. Hence in this region, viscous effects dominate the flow. However, as we reach the parabolic velocity profile, the largest gradients are only at the wall resulting in higher shear stress. Due to the parabolic profile, the shear stresses decrease as you get closer to the centerline and eventually become zero.
Assuming that the flow is Newtonian, the wall shear stress at any instant of time is given by

To answer your question: During the initial stages of the flow, the thickness of the boundary layer is small and wall shear stress is the highest due to rapidly changing gradients. Hence in this region, viscous effects dominate the flow. However, as we reach the parabolic velocity profile, the largest gradients are only at the wall resulting in higher shear stress. Due to the parabolic profile, the shear stresses decrease as you get closer to the centerline and eventually become zero.
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