The velocity distribution in laminar flow through a circular pipe follows the parabolic law.

Laminar flow refers to the smooth and orderly flow of a fluid through a pipe or channel. In this type of flow, the fluid moves in parallel layers, with each layer sliding smoothly over the adjacent layers. The velocity distribution describes how the velocity of the fluid varies across the cross-section of the pipe.

Explanation:
The velocity distribution in laminar flow through a circular pipe follows the parabolic law. This means that the velocity of the fluid is highest at the center of the pipe and decreases gradually towards the walls. The velocity profile can be represented by a parabolic curve.

Reasoning:
The parabolic velocity distribution in laminar flow through a circular pipe can be explained by the concept of viscosity. Viscosity is the internal friction within a fluid that resists its flow. In laminar flow, the fluid layers slide smoothly over each other, and the frictional forces between the layers are dominant.

As the fluid flows through the pipe, the fluid molecules near the center experience less friction compared to the ones near the walls. This is because the fluid near the walls is in contact with the rough surface of the pipe, which increases the frictional forces. As a result, the fluid near the walls moves at a slower velocity compared to the fluid near the center.

The parabolic velocity distribution arises due to the balance between the pressure gradient and the viscous forces acting on the fluid. The pressure gradient causes the fluid to accelerate, while the viscous forces resist the flow. The parabolic velocity profile is the result of this balance, where the maximum velocity occurs at the center of the pipe where the pressure gradient is highest.

Conclusion:
In conclusion, the velocity distribution in laminar flow through a circular pipe follows the parabolic law. This parabolic velocity profile is a result of the balance between the pressure gradient and the viscous forces within the fluid. Understanding the velocity distribution is important for various engineering applications, such as designing pipes and predicting flow rates.