To determine the mass flow rate of air required for the gas turbine, we can use the energy balance equation. The power produced by the gas turbine is equal to the energy input minus the heat loss.
Given: Power output (P) = 3000 hp = 3000 * 745.7 W = 2,237,100 W Inlet temperature (T1) = 650 K Heat loss (Q_loss) = 70 kJ/s = 70,000 W Exhaust temperature (T2) = 2000 °C = 2000 + 273.15 K = 2273.15 K
The energy balance equation is given by: P = m_dot * Cp * (T2 - T1) - Q_loss
Where: m_dot is the mass flow rate of air Cp is the specific heat capacity of air at constant pressure
To simplify the calculation, we can assume that the specific heat capacity of air (Cp) remains constant within the given temperature range. Cp for air is approximately 1005 J/(kg·K).
Rearranging the equation and solving for m_dot, we have: m_dot = (P + Q_loss) / (Cp * (T2 - T1))
Substituting the given values: m_dot = (2,237,100 + 70,000) / (1005 * (2273.15 - 650))
Calculating the expression: m_dot ≈ 230.98 kg/s
Therefore, the mass flow rate of air required for the gas turbine is approximately 230.98 kg/s.