The slope of the energy grade line (S) is a crucial parameter in fluid mechanics, particularly in the analysis of energy distribution and losses in open-channel flow or pipe flow systems. The slope of the EGL, denoted by S, indicates the rate of change of total head with respect to the length of the flow path. Mathematically, the slope of the energy grade line can be calculated using the following formula:

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Where:

• $S$ is the slope of the energy grade line.
• $\Delta h$ is the change in total head along the flow path.
• $L$ is the length of the flow path.