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Analysis of Radial Flow Reaction Turbines Key Equations governing analysis of turbines.

Calculation of Flow Rate, Q: Q = 2π r₁ b₁ V_r1 = 2π r₂ b₂ V_r2 V_r1 , V_r2 in ft/sec or m/sec

where r₂ is the radial distance to the exit and b₂ is the height at the exit in ft or in m

r₁ is the radial distance to the entrance and b₂ is the height at the entrance

V_r2 is the radial component of the absolute velocity of the fluid at the exit

V_r1 is the radial component of the absolute velocity of the fluid at the entrance

Q is the flow rate in ft³/sec or in m³/sec

Entrance means the leading edge of the vane and exit means the trailing edge of the vane.

External torque extracted from the fluid: T_z = ρ Q [( r₂ V_t2 ˗ r₁ V_t1 ]

where ρ Q is the mass flow rate crossing the control surface (It is the same

entering and leaving the control surface). ρ Q = dm/dt

r₂ V_t2 where r₂ is the radial distance to the exit on the vane and V_t2 is the tangential

component of the absolute fluid velocity of the fluid particle at the exit

r₁ V_t1 where r₁ is the radial distance to the entrance on the vane and V_t1 is the tangential

component of the absolute fluid velocity of the fluid particle at the entrance

T_z is the external torque driving the impeller in ft lb or in N m

Power extracted from the fluid by the turbine: P= T_z ω

where: T_z is the external torque driving the impeller in ft lb or N m

ω is the angular speed of the impeller in rad/sec

P is the power generated in ft lb/sec or N m / sec

Head extracted from the fluid by the turbine: H = P / Q γ (H is a positive value.)

where: P is the power added to the fluid in ft lb/sec or Nm /sec

Q is the flow rate in ft³/sec or m³/sec

γ is the specific weight of the fluid in lb/ft³ or in N/m³

H is the head added to the fluid in ft or in m

Pressure drop: ∆P = P₁ ˗ P₂ = γ H + (1/2)ρ V₂² ˗ (1/2) ρ V₁ ² (From energy equation)

∆P is in lb/ft² or in N/m² ρ is in slugs/ft³ or in kg/m³ V₁ and V₂ in ft/sec or in m/sec