Solution Found!
Figure 13.9 shows a fluid flow where the flow is
Chapter 13, Problem 13.30(choose chapter or problem)
Figure 13.9 shows a fluid flow where the flow is everywhere outward (at least for all points on the surface S shown). This means that all contributions to the change 8V in volume are positive, and V is definitely increasing. Sketch the corresponding picture for the case that the flow is outward on the upper part of S and inward on the lower part. Explain clearly why the contributions n v 8t dA to the change in V from the lower part of S are negative, and hence that 8V can be of either sign, depending on whether the positive contributions outweigh the negative or vice versa.
Questions & Answers
QUESTION:
Figure 13.9 shows a fluid flow where the flow is everywhere outward (at least for all points on the surface S shown). This means that all contributions to the change 8V in volume are positive, and V is definitely increasing. Sketch the corresponding picture for the case that the flow is outward on the upper part of S and inward on the lower part. Explain clearly why the contributions n v 8t dA to the change in V from the lower part of S are negative, and hence that 8V can be of either sign, depending on whether the positive contributions outweigh the negative or vice versa.
ANSWER:Step 1 of 3
From sketch below it is clear that there are positive contributions and negative contributions
Where 
