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Our lecturer explained us the Reynold Transport theorem, its derivation , but I don't get where the - sign in control surface 1 comes from? He said that the Area goes in opposite direction compared with this system.

I can't visualise this on our picture.

Can you please help me understand why we have the negative sign on the control surface 1 and at the end of the theorem we have +ve everywhere?

The pictures are attached below

Fig1-Illustrates the - sign enquiry with regards to control surface 1. Why is it - here? and not +

Fig2-Illustrates the final form of the Reynolds Transport theorem where all signs are +, why?

How to know when the Area is in same direction as the system velocity ? and how to know when the Area goes opposite direction with regards to the system velocity?

Thank you in advance.

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# Reynolds Transport Theorem Derivation Sign Enquiry

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