Final answer:
The maximum velocity of the fluid in the circular pipe is equal to the average velocity, which can be calculated by dividing the volumetric flow rate by the cross-sectional area of the pipe. By setting the product of the maximum velocity and the cross-sectional area equal to the product of the average velocity and the cross-sectional area, we can solve for the maximum velocity at the section. In this case, the maximum velocity is approximately 2.5 m/s.
Step-by-step explanation:
In fluid dynamics, the relationship between the velocity and cross-sectional area of a fluid flowing through a pipe is described by the principle of continuity, which states that the product of velocity and cross-sectional area is constant.
Using this principle, we can find the maximum velocity of the fluid at a section of the circular pipe by setting the product of the maximum velocity and the cross-sectional area of the pipe equal to the product of the average velocity and the cross-sectional area at that section.
The average velocity can be calculated by dividing the volumetric flow rate of the fluid by the cross-sectional area of the pipe.
Given that the volumetric flow rate is 0.05 m³/s and the diameter of the pipe is 0.16 m, we can calculate the cross-sectional area as 0.0201 m².
By dividing the volumetric flow rate by the cross-sectional area, we can find the average velocity as 2.48 m/s.
Now, setting the product of the maximum velocity and the cross-sectional area equal to the product of the average velocity and the cross-sectional area, we can solve for the maximum velocity at the section:
Maximum velocity * cross-sectional area = average velocity * cross-sectional area
Maximum velocity = (average velocity * cross-sectional area) / cross-sectional area
Maximum velocity = average velocity = 2.48 m/s
Therefore, the maximum velocity at the section is most nearly 2.5 m/s (option B).