Question

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Pictured to the left is a basic schematic of an inflatable air dancer advertiser. A pump with a total energy grade line of hp (labeled a) is attached to a blower (labeled B) that shoot air into the air dancer which is ejected through a nozzle at its top (labeled C). The blower has Re : h Raknown radius of R and the nozzle has a known radius at its end of R. Assuming all geometry and fluid properties are known, the fluid is incompressible, frictional losses are negligible, the total energy of the pump (hp) is known, and the problem is steady state, answer the following questions. A) Find the average velocities at points b and c (Vb and Vc) in terms of known variables. NOTE: Finding Vb in terms of Vc, or vice versa, is only acceptable if one of those velocities is solved for in terms of other known geometries, pressures, or total head. B) Assuming Vc and Vb are now known, solve for the pressure at point b in terms of known velocities, geometry and fluid properties. C) The velocities solved for in part A are the average velocities. Assume the actual velocities at b and c follow this equation: V(r)-%verage * (1-R) Using the above equation, find the net force to keep the air dancer in equilibrium due to the change in momentum of the fluid. Use the air dancer as a control volume. You do not have to substitute in results for quantities solved for in part a or b (i.e. using Vais fine. NOTE: f? da = 2m(? r dr.

Answer 1

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