Liquid Rocket Injector Orifice Cd Calculator
Liquid rocket propulsion engineering: Determine injector orifice discharge coefficient ($C_d$), differential injection pressure drop ($\Delta P$), and impinging stream droplet atomization ($SMD$).
Injector Element Geometry
Individual drill hole diameter
Typical injector face thickness ~3–6 L/d
Fluid & Injection Pressures
LOX ~1140, Kerosene ~810, Methane ~422 kg/m³
Pressure drop across injector face
Used for ΔP/Pc combustion stability check
Bernoulli Injection Orifice Equation
Mass flow through a liquid injector orifice is governed by:
$$\dot{m} = C_d \cdot A \cdot \sqrt{2 \rho \Delta P}$$
Where $C_d = C_c \cdot C_v$ combines the vena contracta contraction coefficient and viscous losses. The rule of thumb $\Delta P / P_c \ge 15\% - 20\%$ prevents chug combustion instability.
Orifice Hydraulics & Mass Flow
Discharge Coefficient (C_d)
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Total Mass Flow Rate (ṁ)
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Flow Velocity & Droplet Atomization
Jet Exit Velocity (v_jet)
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Ideal: √(2·ΔP/ρ)
Sauter Mean Diameter (SMD)
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Impinging doublet droplet D₃₂
Combustion Stability Margin
Stiffness Ratio (ΔP / P_c):
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Flow per Individual Orifice:
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Cavitation / Separation State:
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Chug Stability Evaluation:
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