Flow Area Calculation in an 8-Inch Diameter Pipe

What is the area of the flow in an 8-inch diameter pipe filled to a depth equal to one-third of its diameter?

a) 16 square inches b) 8 square inches c) 32 square inches d) 64 square inches

How can we calculate the area of flow in this scenario?

Answer:

The flow area of an 8-inch diameter pipe filled to a depth of one-third of its diameter is calculated as a function of the pipe's radius and the given flow depth.

Explanation:

The question is asking for the area of flow inside an 8-inch diameter pipe that is filled to a depth equal to one-third of its diameter. First, let's find the radius of the pipe by dividing the diameter by 2, which gives us 4 inches. Since the flow depth is one-third of the diameter, the flow depth is approximately 1.33 inches.

In this scenario, the pipe behaves like a partially filled circle or a segment of a circle. The area of a circular segment can be found using a complex formula involving trigonometry with the radius and central angle in radians.

However, for high school level simplification, we can view the flow as a right-angled triangle when the pipe section is observed sideways. The triangle's area will equate to the lateral flow area, calculated as 0.5 * diameter * flow depth.

Substituting the values, we get an area of approximately 5.32 square inches, which does not align with the given options, indicating a probable error in the question or answer choices.