What uniform flow velocity conversion occurs when sloping pipe changes from 1/4 in/ft to 1/8 in/ft slope?

In fluid mechanics and plumbing design, when examining the relationship between pipe slopes and flow velocities, it's important to understand how the slope of a pipe influences gravitational potential energy and, in turn, flow dynamics. The flow velocity in a pipe can be related to the slope by Bernoulli's equation and other hydrodynamic principles.

In this particular question, you have a change in the slope of a pipe from 1/4 inch per foot to 1/8 inch per foot. The relationship between slope and flow velocity can be described through the concept of gravitational potential energy changing due to the different slopes in the piping system.

When the slope is reduced from 1/4 in/ft to 1/8 in/ft, it indicates a lower potential energy gradient, which affects the flow velocity. The conversion of flow velocity based on slope is represented under the assumption of uniform flow where a ratio is derived based on the square root of the slopes.

To find the conversion factor, you would take the ratio of the square roots of the slopes. The old slope would be represented as (1/4) and the new slope as (1/8). This results in the conversion factor for velocities calculated as follows:

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