To understand the concept of the proportional perimeter of a circular sewer, let's break down the given information and analyze it step by step.



The central angle, denoted as K, is the angle subtended at a circular section of the sewer. This means that K is the angle formed at the center of the circle, with the two sides of the angle intersecting the circular section of the sewer.



The proportional perimeter of the circular sewer refers to the portion of the total circumference of the circle that is covered by the sewer. In other words, it represents the length of the sewer relative to the entire circumference of the circle.



To calculate the proportional perimeter, we need to determine the ratio of the central angle to the total angle of a circle, which is 360 degrees.

Let's assume the proportional perimeter is P.

We can set up the following proportion:

P / 2πr = K / 360 degrees

Where:
- P is the proportional perimeter
- π is the mathematical constant pi (approximately 3.14159)
- r is the radius of the circular sewer
- K is the central angle subtended at the circular section of the sewer
- 360 degrees is the total angle of a circle

Simplifying the proportion, we get:

P = (2πr * K) / 360 degrees

Since we are looking for the proportional perimeter as a fraction of the total circumference, we can simplify further:

P = (2πr * K) / 360 degrees = (πr * K) / 180 degrees

Now, we can observe that the expression (πr * K) / 180 degrees is equivalent to K / 180 degrees times πr, which represents the ratio of the central angle to the total angle of a circle.

Therefore, the proportional perimeter of a circular sewer running partially half where K is the central angle subtended at a circular section of the sewer is K/360 degrees.