Form for the written test v1

Pagina 1

WATERJET • Equilibrium forces in the pump: 𝑃𝑤𝑎𝑡𝑒𝑟𝑆𝑤𝑎𝑡𝑒𝑟 = 𝑃𝑜𝑖𝑙𝑆𝑜𝑖𝑙 • Pressure of the water after the pump: 𝑃𝑤𝑎𝑡𝑒𝑟 = 𝑆𝑜𝑖𝑙 𝑆𝑤𝑎𝑡𝑒𝑟 𝑃𝑜𝑖𝑙 • Intensification factor: 𝑆𝑜𝑖𝑙 𝑆𝑤𝑎𝑡𝑒𝑟 ≅ 20 • Equation theorical waterjet velocity for a compressible flow: 𝑣𝑡ℎ,𝑐 2 2 + ∫ 𝜕𝑃 𝜌𝑤 = 𝑐𝑜𝑛𝑠𝑡 • Water density at a certain 𝑃 pressure: 𝜌𝑤 𝜌0 = (1 + 𝑃 𝐿) 𝑛 𝐿 = 300𝑀𝑝𝑎 𝑛 = 0,1368 • Theorical waterjet velocity for a compressible flow: 𝑣𝑡ℎ,𝑐 [ 𝑚 𝑠 ] = √ 2𝐿 (1−𝑛)𝜌0 [(1 + 𝑃 𝐿) 1−𝑛 − 1] • Theorical waterjet velocity for an incompressible flow: 𝑣𝑡ℎ [ 𝑚 𝑠 ] = √ 2𝑃 𝜌0 • Compressibility coefficient: 𝜓 = 𝑣𝑡ℎ,𝑐 𝑣𝑡ℎ = √ 𝐿 𝑃(1−𝑛)[(1 + 𝑃 𝐿) 1−𝑛 − 1] • Jet velocity after the frictional losses (real water jet velocity outflowing the primary orifice): 𝑣𝑗 [ 𝑚 𝑠 ] = 𝐶𝑣𝑣𝑡ℎ,𝑐 = 𝐶𝑣𝜓𝑣𝑡ℎ • Velocity coefficient: 𝐶𝑣 = 𝑣𝑗 𝑣𝑡ℎ,𝑐 • Contraction coefficient: 𝐶𝑐 = 𝑆𝑗 𝑆0 • Area that correspond to the nominal diameter (diameter of the orifice 𝑑𝑛 = 𝑑0): 𝑆0 = 𝜋𝑑02 4 • Area that correspond to the minimum diameter (minimum diameter 𝑑𝑗): 𝑆𝑗 = 𝜋𝑑𝑗 2 4 • Water mass flow rate: 𝑚̇ 𝑤 [ 𝑘𝑔 𝑠 ] = 𝑄𝑤𝜌0 • Real volumetric flow rate: 𝑄𝑤 = 𝐶𝑑𝑆0𝑣𝑡ℎ • Theoretical volumetric flow rate: 𝑄𝑡ℎ = 𝑆𝑜𝑣𝑡ℎ • Overall coefficient of discharge: 𝐶𝑑 = 𝑄𝑤 𝑄𝑡ℎ = 𝜓𝐶𝑣𝐶𝑐 • Jet reactive force: 𝐹 = 𝑚̇ 𝑤2𝑣𝑗 = 𝜋 2 𝐶𝑐𝐶𝑣2 𝜓2𝑑𝑛2𝑃 Density of water at ambient temperature 𝜌0 = 1000𝑘𝑔 𝑚3 • Thrust force: 𝑆 = 𝑚̇ 𝑤(𝑣𝑗 + 𝑣𝑟𝑒𝑓) cos 𝜗 = (𝑚̇ 𝑤 + 𝑚̇ 𝑎)𝑣𝑎𝑤𝑗2 cos 𝜗 • Hydraulic power: 𝑃ℎ𝑦𝑑𝑟[𝑀𝑃𝑎] = 1 2 𝑚̇ 𝑤𝑣𝑗 2 = 𝜋 √8𝜌0 𝐶𝑐𝐶𝑣3𝜓3𝑑𝑛2𝑃1,5 = 𝑄𝑤𝑃 • Electrical power: 𝑃𝑒𝑙 = 𝑄𝑤 ∙ 𝑃[𝑀𝑃𝑎] 𝜂𝑒𝑙 • Sound velocity in water: 𝑣𝑠 = √ 𝐿 𝑛𝜌0 (1 + 𝑃 𝐿) 1−𝑛 2 • Maximum possible increase of temperature in the catcher: Δ𝑇 = 𝐶𝑣2𝜓2𝑃 𝑐𝑝𝜌0 • Pressure loss: 𝜕𝑃 𝜕𝑡 = √2𝐶𝑐𝐶𝑣𝑆0 √𝜌0𝑉0 𝐾𝑤𝜓𝑃1,5 • Water stiffness: 𝐾𝑤 • Reaction force: 𝐹 = 𝑚̇ 𝑤𝑣𝑗 = 𝜌0𝑄𝑤𝑣𝑗 ABRASIVE WATERJET • mixed jet velocity outflowing the focuser 𝑣𝑎𝑤𝑗 = ( 1 1+𝑟)…