Question about formulas in fluids

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In fluid dynamics, when applying Bernoulli's equation and momentum principles, gauge pressure is typically used, omitting atmospheric pressure from calculations. This is because when both pressures are atmospheric, they cancel each other out, simplifying the equation. However, even when one pressure is atmospheric and the other is not, atmospheric pressure is still disregarded in calculations. The rationale is that it can be subtracted from both sides of the equation, maintaining balance. This approach streamlines the analysis without losing accuracy in pressure differences.
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When using bernoullis and momentum, gauge pressure is only used in calculations, any atmospheric pressure is generally omitted, i could understand if, for example, using bernoullis, pressure 1 and pressure 2 were both atmospheric, therefore they would cancel out, but when one pressure is atmospheric and another if different it is still omitted. Why is this?
 
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Because atmospheric pressure can still be subtracted out on both sides of the equation.
But you can't have it on one siode and not the other.
 

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