B Fluid Continuity Equation in different reference frame

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The discussion centers on the application of the continuity equation in fluid dynamics, specifically regarding changes in fluid velocity and cross-sectional area. When fluid velocity increases, the area must decrease to maintain continuity, but switching to a different reference frame complicates this relationship. The key point is that the area constriction is relative to the tube's reference frame, not an arbitrary frame of reference. Understanding this is crucial for correctly applying the continuity equation. The derivation of the continuity equation clarifies these relationships and resolves the apparent violation.
versine
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If I have fluid with area 10 and velocity 10, if the velocity increases to 20 the area will become 5. But if we switch to a reference frame moving at velocity 1 opposite this motion, then it would be 10 and 11 to 5 and 21, violating the continuity equation. What is wrong?
 
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If I understand what you ask correctly, the area is constricted because the fluid is moving through some tube. If that's the case, it's the velocity relative to the tube's reference frame that counts. You will see why if you follow the derivation of the continuity equation.
 
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