If the diameter of a drain is doubled, how will this affect the force applied to a test plug?

When the diameter of a drain is doubled, the area of the circular opening increases with the square of the diameter. The relationship between the diameter and the area can be expressed by the formula for the area of a circle, A = π(d/2)², where d is the diameter. If the diameter is doubled, we can analyze the area as follows:

1. If the initial diameter is d, the area is A1 = π(d/2)².

2. If the diameter is doubled to 2d, the new area becomes A2 = π((2d)/2)² = π(d)², which equals four times the original area (since (2d/2)² = (d)²).

Therefore, when the diameter doubles, the area through which the force is applied also increases by a factor of four. This increased area means that for the same amount of pressure or force, the total force exerted on a test plug is now four times greater. As a result, when considering how the force applied to a test plug changes as a function of the diameter, it will increase fourfold when the diameter is doubled.