- Asked 2/15
- 2073 Bhadra · 8 marks
- 2071 Bhadra · 8 marks
Adiabatic air turbine: mass flow and areas
Short answer
Mass flow rate is found from steady-flow energy: ṁ = 3600 / [1.005(1000-400) + (10² - 100²)/2000] = 6.02 kg/s. Using ideal gas specific volumes, inlet area A₁ = 0.173 m² and exit area A₂ = 0.0691 m².
Air expands through an adiabatic turbine from 1000 KPa, 1000 K to 100 KPa, 400K. The inlet velocity is 10 m/s whereas exit velocity is 100 m/s. The power output of the turbine is 3600 KW. Determine the mass flow rate of air, the inlet and the exit area. [Take R = 287 J/KgK and Cp = 1005 J/KgK]
Given: adiabatic turbine, air: P₁ = 1000 kPa, T₁ = 1000 K, V₁ = 10 m/s; P₂ = 100 kPa, T₂ = 400 K, V₂ = 100 m/s; Ẇ = 3600 kW; R = 0.287, c_p = 1.005 kJ/kg·K.
Steady-flow energy equation (Q = 0, ΔPE = 0):
Ẇ = ṁ [ c_p (T₁ − T₂) + (V₁² − V₂²)/2 ]
Step 1: Mass flow rate
c_p (T₁ − T₂) = 1.005 × 600 = 603.0 kJ/kg
(V₁² − V₂²)/2 = (100 − 10 000)/2 = −4950 J/kg = −4.95 kJ/kg
Work per kg = 603.0 − 4.95 = 598.05 kJ/kg
ṁ = 3600/598.05 = 6.02 kg/s
Step 2: Specific volumes (ideal gas)
v₁ = RT₁/P₁ = 0.287 × 1000/1000 = 0.287 m³/kg
v₂ = RT₂/P₂ = 0.287 × 400/100 = 1.148 m³/kg
Step 3: Areas (ṁ = A V/v)
A₁ = ṁ v₁/V₁ = 6.02 × 0.287/10 = 0.1728 m²
A₂ = ṁ v₂/V₂ = 6.02 × 1.148/100 = 0.0691 m²
Answer: ṁ = 6.02 kg/s; A₁ = 0.173 m²; A₂ = 0.0691 m².
✓ Answer checked by Claude Opus 5.5 (high effort)
Related questions
- Steam nozzle 4 MPa: mass flow, exit velocity, area · Fundamental of Thermodynamics & Heat Transfer, chapter 4
- Adiabatic steam turbine 50 MW: mass flow, isentropic efficiency · Fundamental of Thermodynamics & Heat Transfer, chapter 5
- Air nozzle: exit temperature and exit area · Fundamental of Thermodynamics & Heat Transfer, chapter 4
- Gas turbine 60 MW: heat loss and areas · Fundamental of Thermodynamics & Heat Transfer, chapter 4
- Ideal gas turbine 100 kW: pressure ratio, work, efficiency · Fundamental of Thermodynamics & Heat Transfer, chapter 6
- Adiabatic diffuser: exit temperature and pressure · Fundamental of Thermodynamics & Heat Transfer, chapter 4
- Gas turbine 800 kW with regenerator · Power Plant Equipment, chapter 6 · asked 2×
- Francis turbine velocity triangles and power · Fluid Machines, chapter 3
- Convergent nozzle: choking and mass flow · Turbo Machines, chapter 4
- Gas turbine power from isentropic efficiency · Turbo Machines, chapter 1
All Fundamental of Thermodynamics & Heat Transfer chapter 4 questions →