Water (left(60{ }^{circ} mathrm{F} ight)) flows through an annular space formed by inserting a 1 -in.-radius solid

Water \(\left(60{ }^{\circ} \mathrm{F}\right)\) flows through an annular space formed by inserting a 1 -in.-radius solid cylinder into a 1.5-in.-radius tube. The following axial velocities were measured in the annular space.

Assume that the no-slip condition \((u=0)\) exists at the solid boundaries. What are the rates of mass, momentum, and kinetic energy flow through the annular space?

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(r-r)/(ro-r) 0.1 u (ft/s) 12 0.2 23 0.3 28 0.4 33 0.5 34 0.6 31 0.7 28 0.8 21 0.9 10