13.6 no 3

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OK, the problem here is a practical one.  The "flow outward" this problem wants is in the units kg/sec. Since the density is kg/m^3,  and since the vector field v is in m/sec, and since dS has units m^2, the product density*v.dS has units of kg/sec.  Thus the rate of flow outward will be

5∫v.dS=5x(8/3)pi

 or (40/3)Pi.