Maximizing Efficiency: Understanding Hydraulic Radius in Pipes
Which pipe has the larger hydraulic radius and by what percentage?
Given that two pipes, one circular and one square, have the same cross-sectional area, which pipe will have the larger hydraulic radius and by what percentage?
Final Answer:
The circular pipe will have a larger hydraulic radius compared to the square pipe.
Explanation:
The hydraulic radius of a pipe is a crucial factor in determining the efficiency of flow within the pipe. In this case, the circular pipe will have a larger hydraulic radius compared to the square pipe. To calculate the percentage difference between the two hydraulic radii, we can use the formula: Percentage Difference = ((Rc - Rs) / Rc) * 100%.
Understanding Hydraulic Radius in Pipes
Hydraulic radius is a key parameter used in fluid mechanics to evaluate the efficiency of flow in pipes. It is defined as the cross-sectional area of flow divided by the wetted perimeter of the pipe.
When comparing a circular pipe to a square pipe with the same cross-sectional area, the circular pipe will have a larger hydraulic radius. This is because the circular shape minimizes the wetted perimeter compared to the square shape, resulting in a more efficient flow.
To calculate the hydraulic radius for each pipe, the formula R = A / P is used, where R is the hydraulic radius, A is the cross-sectional area, and P is the wetted perimeter. By substituting the values for the cross-sectional areas of the circular and square pipes, we can determine the hydraulic radii for each and calculate the percentage difference between them.