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A 90° elbow is installed on a return line of a tank open to atmosphere. The areas at the elbow entrance and exit are respectively 5 and 3 cm². The return flow rate is 50 l/min. The pressure at the elbow entrance is 1 bar. Determine the overall force acting on the connecting bolts, assuming that no load is transmitted to piping upstream the elbow. Consider the frictional effects in the elbow negligible. The volume of the fluid contained in the elbow is 70 cm³.

Given:

Flow rate Q = 50 l/min; elbow entrance cross‐sectional area A₁ = 5 cm²; elbow exit area A₂ = 3 cm²; elbow turning angle α = 90°; tank pressure p₂ = p_atm = 1 bar; pressure at elbow entrance p₁ = 1 bar; volume of the fluid in the elbow V = 70 cm³; fluid density ρ = 870 kg/m³

Find:

Forces acting on the elbow, F_x, F_y;