Why there is a difference between same components of 2 paral

Hawkingo · Dec 29, 2018

Figure 10.2: a rectangular box element with edges labelled dx, dy and dz along the x, y and z axes, with faces numbered 1 and 2 on opposite sides along the x direction.

Printed textbook page with text and equations: the difference in Vx between two surfaces, dVx = (∂Vx/∂x) dx, and the net outflow expression (10.5) [(Vx at surface 2) - (Vx at surface 1)]dy dz = (∂Vx/∂x dx) dy dz.

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;

Printed page of text with equations (10.2) to (10.4) on water flow: amount crossing area A' equals vtA'p, and vp cos θ = V cos θ = V · n, with a figure reference to Figure 10.1.

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 · Dec 30, 2018

Hawkingo said:

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 · Dec 30, 2018

Hawkingo said:

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.

Why there is a difference between same components of 2 paral

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