How does hose diameter affect friction loss at a given pressure and flow rate?

The relationship between hose diameter and friction loss is based on hydraulic principles. When you consider the diameter of the hose, a larger diameter hose allows water to flow more freely with less resistance, while a smaller diameter hose causes more friction as water moves through it.

Friction loss is directly related to both the length and diameter of the hose, as per the Darcy-Weisbach and Hazen-Williams formulas. A smaller diameter results in increased friction loss because the water faces greater resistance due to the reduced cross-sectional area. Consequently, if you maintain a constant pressure and flow rate, a smaller diameter will lead to higher friction loss compared to a larger diameter.

In contexts of hose length, friction loss will increase with a longer hose, but the key aspect here is that with a smaller diameter, you're inherently increasing the friction loss. Thus, at any given pressure and flow rate, using a smaller diameter hose will indeed lead to a longer friction loss when compared to a larger diameter hose, affirming the relationship that leads to option B being the correct choice.