De Laval Turbine — Slider Calculator

Inputs

Inlet pressure p₁ (bar)

Inlet temperature T₁ (°C)

Exit pressure p₂ (bar)

Nozzle angle α (deg from tangent)

Mechanical efficiency ηₘₑcₕ

Mean rotor diameter d (m)

Mass flow ṁ (kg/s)

cₚ (superheated steam) (kJ/kg·K)

Key Results

Isentropic heat drop Δh (kJ/kg)

—

Jet speed C₁ (m/s)

—

Optimum tip speed u (m/s)

—

Speed N (rpm)

—

Shaft work w_shaft (kJ/kg)

—

Power P (kW)

—

Outlet dryness x (–)

—

Water content w = 1−x

—

h₂s (kJ/kg)

—

Method: Δh is estimated from an isentropic expansion using simplified steam relations (latent heat fit and ideal‑gas superheat). For design‑grade work use steam tables/IAPWS‑IF97.

Details & equations

Tsat(p) ≈ 100 + 22 ln(p_bar); h_f(T)≈c_plT; s_f(T)≈c_plln(T_K/273.15); L(T)≈2501−2.36(T−100); h_g=h_f+L; s_g=s_f+L/T_K; Superheat: h₁≈h_g(T_sat1)+c_p(T₁−T_sat1), s₁≈s_g(T_sat1)+c_pln(T₁/T_sat1). At p₂: x=(s₁−s_f2)/(s_g2−s_f2), h₂s=h_f2+x·L₂, Δh=h₁−h₂s. Nozzle/rotor: C₁=√(2Δh·1000); C_1θ=C₁cosα; u_opt=C_1θ/2; N=60u/(πd); w_stage=Δh cos²α; w_shaft=η_mech·w_stage; P=ṁ·w_shaft.

De Laval Turbine — Slider Calculator educational approx

Inputs

Key Results

Isentropic heat drop Δh (kJ/kg)

Jet speed C₁ (m/s)

Optimum tip speed u (m/s)

Speed N (rpm)

Shaft work wshaft (kJ/kg)

Power P (kW)

Outlet dryness x (–)

Water content w = 1−x

h₂s (kJ/kg)

Details & equations

Shaft work w_shaft (kJ/kg)