Which of the following is NOT an assumption of the Streeter-Phelps Oxygen Sag Equation?

The assumption regarding the initial deficit equals zero is indeed not part of the Streeter-Phelps Oxygen Sag Equation. In reality, the equation is used to model the dissolved oxygen levels in a water body downstream from a pollution source, and it typically considers various scenarios including pre-existing conditions of dissolved oxygen.

The other assumptions involved are integral to the application of the equation. First, the assumption that the stream is well-mixed ensures that the calculations reflect an average condition throughout the water column, which is essential for accurate modeling of oxygen levels. If mixing were inadequate, the results could be skewed due to localized variations in oxygen content.

Secondly, the assumption that decomposition rates are constant enables straightforward calculations of oxygen demand over time and distance in the water body. Fluctuating rates would complicate the model significantly and could lead to inaccurate predictions of oxygen depletion.

Finally, the assumption that the only source of oxygen is atmospheric diffusion simplifies the analysis, although in practice, there may be other sources or sinks of oxygen (such as photosynthesis or respiration) that could influence the overall dissolved oxygen levels. Thus, the primary focus remains on atmospheric diffusion as a theoretical basis for developing the oxygen sag curve.

In summary, identifying the initial deficit as zero is not an inherent