Non-Traditional Machining, Cold-Cutting Abrasive Waterjet (AWJ) & UHP Intensifier Pumps
Abrasive Waterjet (AWJ) Jet Velocity & Pump Power Formula
Calculate Supersonic Ruby/Diamond Orifice Waterjet Velocity (m/s), Vena-Contracta Orifice Water Flow (L/min), Hydraulic Jet Power (kW), and Garnet-to-Water Mass Loading Ratio.
At 3,800–6,000 bar, a jewel waterjet orifice fires water at Mach 2.5–3.0 in air—and hydraulic power scales with P^(1.5)!
Cold-cutting titanium aerospace plates, stone, or carbon-fiber composites without a heat-affected zone (HAZ) expands Ultra-High-Pressure (UHP) water (`P = 3,800–6,000` bar = `380–600` MPa) through a tiny `0.25–0.38` mm sharp-edged ruby or diamond jewel orifice (`A_0 = (PI()/4) * d_0^2`)! Bernoulli conversion with Compressibility/Friction Velocity Coefficient `C_v` (`~0.94–0.97`) accelerates the coherent water core to supersonic `v_jet = C_v * SQRT((2 * P_Pa) / rho_w)` (`> 800–1,050` m/s, ~`2.5–3.0x` the speed of sound in air!). Because sharp jewel edges form a vena contracta (`C_c ≈ 0.70`), Total Discharge Coefficient `C_d = C_v * C_c` (`~0.65–0.72`) limits Orifice Water Consumption to `Q = C_d * A_0 * SQRT((2 * P_Pa) / rho_w)`—meaning Hydraulic Jet Power `P_hyd = P * Q` grows with `P^(1.5) * d_0^2`! Inside the Venturi mixing chamber, `80`-mesh Barton garnet (`dot_m_a`, g/min) entrains at Abrasive-to-Water Mass Ratio `R_aw = (dot_m_a / 1,000) / Q_L_min` (`~0.10–0.16`)!
Verify on a 3,800 bar (`55,000` psi) `0.33` mm (`0.013"`) Diamond-Orifice Cutting Head—Intensifier_Pressure `P` = 3,800.0 bar (B2), Jewel_Orifice_Diameter `d_0` = 0.33 mm (B3), Velocity_Coeff `C_v` = 0.96 (B4 -> Jet Velocity = `836.9` m/s in E2), Orifice_Discharge_Coeff `C_d` = 0.68 (B5 -> Water Flow = `3.04` L/min in E3 & Hydraulic Jet Power = `19.27` kW in E4), and 80-Mesh_Garnet_Feed = 420.0 g/min (B6): Garnet-to-Water Mass Ratio equals `0.138` (E5)!
| UHP Abrasive Waterjet KPI (3,800 bar, d0=0.33 mm Jewel, Cv=0.96, Cd=0.68, 420 g/min) | Formula | Verified Output |
|---|---|---|
| Orifice Waterjet Velocity (m/s) | Cv * SQRT((2 * P_bar * 100000) / 1000) | 836.9 m/s (1,051.6 m/s @ 6,000 bar!) |
| Orifice Water Flow Rate (L/min) | Cd * A_m2 * SQRT(2*P_Pa / 1000) * 60000 | 3.04 L/min (3.82 L/min @ 6,000 bar) |
| Hydraulic Jet Power (kW) | (P_Pa * (Q_L_min / 60000)) / 1000 | 19.27 kW (38.23 kW = +98% @ 6,000 bar!) |
| Garnet-to-Water Mass Ratio Raw | (Garnet_g_min / 1000) / Water_L_min | 0.138 (0.110 @ 6,000 bar) |
Bernoulli Jewel-Orifice Supersonic Jet Power & Garnet Loading Formula
Validate `Pressure` in `[500, 7,000]` bar, `Orifice_Diameter` in `(0.05, 1.5]` mm, `0 < C_d <= C_v <= 1` (discharge coefficient cannot exceed velocity coefficient since `C_c <= 1`!), and `Garnet_Feed >= 0` g/min!
=LET(pr_b, B2, do_m, B3, cv_f, B4, cd_f, B5, gm_m, B6, IF(OR(pr_b < 500, pr_b > 7000, do_m <= 0.05, do_m > 1.5, cv_f <= 0, cv_f > 1, cd_f <= 0, cd_f > cv_f, gm_m < 0), "Invalid AWJ Input", LET(pr_p, pr_b * 100000, ar_m, (PI() / 4) * ((do_m / 1000) ^ 2), ql_m, cd_f * ar_m * SQRT((2 * pr_p) / 1000) * 60000, ROUND((gm_m / 1000) / ql_m, 3))))Hyper-Pressure 6,000 bar (87,000 psi) Intensifier Upgrade Check (Set Pressure B2 = 6,000 bar)
Step up to a `6,000` bar hyper-pressure intensifier (`B2 = 6000`) through the exact same `0.33` mm jewel: Jet Velocity E2 breaks `1` km/s at `1,051.6` m/s (`> Mach 3` in air!), Water Consumption E3 rises to `3.82` L/min, and Hydraulic Jet Power E4 nearly DOUBLES (`(6000/3800)^1.5 = 1.984x`) from `19.27` kW to `38.23` kW!
=IF(ISTEXT(E5), E5, LET(pr_p, B2 * 100000, ar_m, (PI() / 4) * ((B3 / 1000) ^ 2), qs_m, B5 * ar_m * SQRT((2 * pr_p) / 1000), ROUND((pr_p * qs_m) / 1000, 2)))Try the example
Use the original values or change them to test your understanding.