Flag Mechanics> Consider once again the fluid flowing thr...
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Consider once again the fluid flowing through thee pipe described in Problem 14 and illustrated in Fig. 16-41. Find an expression for the mass flux through the annular ring between radii r and r + dr; then integrate this result to find the total mass flux through the pipe, thereby verifying Eq. 16-20.
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

Radhika Batra , 10 Years ago
Grade 11
anser 1 Answers
Kevin Nash
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Last Activity: 10 Years ago
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