Problem

A diffuser is attached to a structure whose rigidity in the horizontal direction can be mo...

A diffuser is attached to a structure whose rigidity in the horizontal direction can be modeled via a linear spring with constant k. The diffuser is hit by a water jet issued with a speed υw = 55 ft/s from a 2 in. diameter nozzle. Assume that the friction between the jet and the diffuser is negligible and that the diffuser’s motion in the vertical direction can be neglected. Recalling that the specific weight of water is γ = 62.4 lb/ft3, if the opening angle of the diffuser is θ = 40°, determine k such that the horizontal displacement of the diffuser does not exceed 0.25 in. from the diffuser’s rest position. Assume that the water jet splits symmetrically over the diffuser.