Introduction:
The ratio of average velocity to maximum velocity is an important parameter in fluid dynamics, particularly when considering the flow of fluids in circular pipes. This ratio can provide insights into the nature and characteristics of the flow. In the case of steady laminar flow in circular pipes, the ratio of average velocity to maximum velocity is 1/2.

Explanation:
To understand why the ratio of average velocity to maximum velocity is 1/2 for steady laminar flow in circular pipes, let's break down the concept:

Steady Laminar Flow:
Steady laminar flow refers to a type of flow in which the fluid moves in smooth layers or streamlines, with no turbulence or mixing. It is characterized by a consistent velocity profile across the pipe cross-section.

Circular Pipes:
Circular pipes are commonly used in fluid transportation systems. The flow in circular pipes can be categorized as laminar or turbulent, depending on the Reynolds number. In the case of steady laminar flow in circular pipes, the flow is smooth and predictable.

Average Velocity:
The average velocity is the mean velocity of the fluid across the pipe cross-section. It is calculated by dividing the volumetric flow rate by the cross-sectional area of the pipe.

Maximum Velocity:
The maximum velocity, also known as the centerline velocity, is the highest velocity that occurs at the center of the pipe. It is typically measured using flow velocity sensors or calculated using theoretical equations.

Ratio of Average Velocity to Maximum Velocity:
In steady laminar flow, the velocity profile across the pipe cross-section follows a parabolic distribution. The velocity is highest at the center and gradually decreases towards the pipe walls. The ratio of average velocity to maximum velocity can be calculated by dividing the average velocity by the maximum velocity.

In the case of steady laminar flow in circular pipes, the velocity profile can be described by the Hagen-Poiseuille equation. This equation relates the average velocity and maximum velocity as follows:

Average velocity = (1/2) * maximum velocity

Therefore, the ratio of average velocity to maximum velocity is 1/2.

Conclusion:
The ratio of average velocity to maximum velocity is an important parameter in fluid dynamics, particularly for steady laminar flow in circular pipes. In this case, the ratio is 1/2, indicating that the average velocity is half of the maximum velocity. This ratio helps in understanding the characteristics of the flow and is used in various engineering calculations and designs related to fluid transportation systems.