B Why there is a difference between same components of 2 paral

[Hawkingo]

In this context the author is deriving the net outflow through 2 surfaces.to do so he is calculating the difference between x components ofthe vector V which is;

so now my question is here the 2 surface are parallel to each other and have same area so their respective x components should be same.so why there is a difference?
thank you.

 

[FactChecker]

the 2 surface are parallel to each other and have same area so their respective x components should be same.so why there is a difference?

Why do you thing they have to be the same? Flow velocity can change from one area to the next.

 

[alan123hk]

View attachment 236565 View attachment 236566
so now my question is here the 2 surface are parallel to each other and have same area so their respective x components should be same.so why there is a difference?
thank you.

The text states that water is flowing either in or out of the volume through each of the six surfaces, so that there is possible difference of velocity between the two surfaces in x-axis, namely some water come in from surface 1 may come out from other surfaces in y or z axis rather than surface 2.