Final answer:
The slope in plumbing is necessary to facilitate gravity-driven flow and prevent blockages, varying based on pipe diameter as large pipes can have a gentler slope while small pipes require steeper ones to maintain flow velocity.
Step-by-step explanation:
The significance of the slope or gradient in horizontal branch piping is crucial for ensuring proper drainage and preventing blockage. The slope facilitates the flow of water and waste through the pipe by gravity, creating a pressure difference that drives the flow. For pipes with a larger diameter, the gradient may be less steep compared to smaller pipes because a larger diameter means there is more surface area for the water to flow across, potentially reducing the speed at which the water flows due to friction. Conversely, smaller pipes require a relatively steeper slope to maintain adequate velocity for waste to avoid settling and causing a blockage.
As per physics and fluid dynamics, the flow rate is directly related to the pressure differential between two points within the piping system. In scenarios like a tapered pipe with differing diameters or a pipe transitioning from a large to a small diameter, the fluid speed increases as the cross-sectional area decreases, due to the conservation of mass. This can be explained by Bernoulli's principle, which states that in a flowing fluid, an increase in speed occurs simultaneously with a decrease in pressure or potential energy.