Water flows out of a big tank along a tube bent at right angles; the inside radius of the tube is equal to r = 0 . 50 cm . The length of the horizontal section of the tube is equal to l = 22 cm . The water flow rate is Q = 0 . 50 L s - 1 . Find the moment of reaction forces of flowing water, acting on the tube's walls, relative to the point Q .

Step-by-step solution

Consider only bend part of the tube. The change in momentum of mass Δm of liquid as it passes through the bend, Δ P → = P → f ⁡ - P → i ⁡ = Δ m ⁡ v ⁡ i ^ - Δ m ⁡ v ⁡ - j ^ = Δ m ⁡ v ⁡ i ^ + Δ m ⁡ v ⁡ j ^ ∴ F → = Δ P ⁡ Δ t = v ⁡ Δ m ⁡ Δ t i ^ + v ⁡ Δ m ⁡ Δ t j ^ = v ⁡ ρ S ⁡ Δ L ⁡ Δ t i ^ + v ⁡ ρ S ⁡ Δ L ⁡ Δ t j ⁡ ^ = ρ S ⁡ v ⁡ 2 i ^ + ρ S ⁡ v ⁡ 2 j ^ ∴ Reaction force on the tube at bend point is F → 0 = - F → ∴ F → 0 = - ρ S ⁡ v ⁡ 2 i ⁡ ^ - ρ S ⁡ v ⁡ 2 j ^ = - ρ π r ⁡ 2 v ⁡ 2 i ^ - ρ π r ⁡ 2 v ⁡ 2 j ^ Moment of the