A square box with dimensions of 5 centimeters is immersed in liquid. Using the g

Question

A square box with dimensions of 5 centimeters is immersed in liquid. Using the given vel. vectors find the avg divergence of flow. They are in centimeters/second. The positive z axis exits through the frontal face, the +x leaves through the right face, and the +y through the top face. Front Vr=30i+60j-30k Right VR=20i-20j+20k Left VL=-100i+200j+300k Top Vr=5i+50j+10k Bottom Vb=0 Back VB=250k My idea was to divide all of these by 5 and insert the dimensional units, so for example front would be Vr=6xi + 12yj-6zk. Then I would take the divergence and then add up all the divergences. But, I have a feeling that I need to make use of Gauss' theorem (the divergence theorem). Any ideas?

Explanation / Answer

front = flux through front surface = Vr.(25k) =-750

right = flux through right surface = VR.(25i) =500

top = flux through top surface = Vr.(25j) =1250

left = flux through left surface = VL.(-25i) =2500

bottom = flux through bottom surface = Vb.(-25j) =0

back = flux through back surface = VB.(-25k) =-6250

Total flux =-740+500+1250+2500+0-6250 = 2750

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