Fluid Continuity Equation in different reference frame

[versine]

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?

 

[kuruman]

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.