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A well-insulated turbine operating at steady state develops 25 MW of power for a steam flow rate of 50 kg/s. The steam enters at 15 bar with a velocity of 61 m/s and exits as saturated vapor at 0.06 bar with a velocity of 130 m/s. Neglecting potential energy effects, determine the inlet temperature, in °C. T1 = i °C

A well-insulated turbine operating at steady state develops 25 MW of power for a steam flow rate of 50 kg/s. The steam enters at 15 bar with a velocity of 61 m/s and exits as saturated vapor at 0.06 bar with a velocity of 130 m/s. Neglecting potential energy effects, determine the inlet temperature, in °C. T1 = i °C

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Problem Statement:** A well-insulated turbine operating at steady state develops 25 MW of power for a steam flow rate of 50 kg/s. The steam enters at 15 bar with a velocity of 61 m/s and exits as saturated vapor at 0.06 bar with a velocity of 130 m/s. Neglecting potential energy effects, determine the inlet temperature, in °C. **Solution:** The given problem can be solved using the principles of thermodynamics, specifically the principles of conservation of energy (First Law of Thermodynamics) for a control volume at steady state. We need to consider the kinetic energy effects and the work interaction of the turbine, but neglect the potential energy effects. Given Data: - Power developed by the turbine (Ẇ_t) = 25 MW = 25,000 kW - Steam mass flow rate (ṁ) = 50 kg/s - Inlet pressure (P_1) = 15 bar - Inlet velocity (V_1) = 61 m/s - Exit condition: saturated vapor at Exit pressure (P_2) = 0.06 bar - Exit velocity (V_2) = 130 m/s To find the inlet temperature (T_1), we need to apply the steady-flow energy equation, which in its basic form is: \[ Ẇ_t + ṁ(h_1 + \frac{V_1^2}{2}) = ṁ(h_2 + \frac{V_2^2}{2}) \] Where: - \( h_1 \) = Enthalpy of the steam at the inlet (to be found using the inlet temperature \( T_1 \)) - \( h_2 \) = Enthalpy of the steam at the exit (saturated vapor at 0.06 bar) **Calculation Steps:** 1. Use steam tables to find the specific enthalpy \( h_2 \) given the saturated vapor condition at 0.06 bar. 2. Re-arrange the steady-flow energy equation to solve for \( h_1 \). 3. Use the steam tables to find the corresponding inlet temperature \( T_1 \) for \( h_1 \). **Numerical Substitution:** Solution: \[ Ẇ_t + ṁ(h_1 + \frac{V_1^2}{2}) = ṁ(h_2 + \
Transcribed Image Text:**Problem Statement:** A well-insulated turbine operating at steady state develops 25 MW of power for a steam flow rate of 50 kg/s. The steam enters at 15 bar with a velocity of 61 m/s and exits as saturated vapor at 0.06 bar with a velocity of 130 m/s. Neglecting potential energy effects, determine the inlet temperature, in °C. **Solution:** The given problem can be solved using the principles of thermodynamics, specifically the principles of conservation of energy (First Law of Thermodynamics) for a control volume at steady state. We need to consider the kinetic energy effects and the work interaction of the turbine, but neglect the potential energy effects. Given Data: - Power developed by the turbine (Ẇ_t) = 25 MW = 25,000 kW - Steam mass flow rate (ṁ) = 50 kg/s - Inlet pressure (P_1) = 15 bar - Inlet velocity (V_1) = 61 m/s - Exit condition: saturated vapor at Exit pressure (P_2) = 0.06 bar - Exit velocity (V_2) = 130 m/s To find the inlet temperature (T_1), we need to apply the steady-flow energy equation, which in its basic form is: \[ Ẇ_t + ṁ(h_1 + \frac{V_1^2}{2}) = ṁ(h_2 + \frac{V_2^2}{2}) \] Where: - \( h_1 \) = Enthalpy of the steam at the inlet (to be found using the inlet temperature \( T_1 \)) - \( h_2 \) = Enthalpy of the steam at the exit (saturated vapor at 0.06 bar) **Calculation Steps:** 1. Use steam tables to find the specific enthalpy \( h_2 \) given the saturated vapor condition at 0.06 bar. 2. Re-arrange the steady-flow energy equation to solve for \( h_1 \). 3. Use the steam tables to find the corresponding inlet temperature \( T_1 \) for \( h_1 \). **Numerical Substitution:** Solution: \[ Ẇ_t + ṁ(h_1 + \frac{V_1^2}{2}) = ṁ(h_2 + \
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