to-air ratio fvert a=0.034 . The take-off gross thrust is F_(g)=34,000 Ibs (151.23 kN) at a flight speed of V_(t-0)=200kts(102m/s) For a choked nozzle that is, an exit Mach number M_(7)=1 and a turbine exit temperature (TET) T_(t,7)=1580F(860^circ C) find: (a) the effective exhaust velocity, (b)the net

To solve this problem, we need to use the given information and apply the appropriate formulas to find the effective exhaust velocity and the net thrust.<br /><br />Given information:<br />- Take-off gross thrust: $F_g = 34,000$ lbs (151.23 kN)<br />- Flight speed: $V_{t-0} = 200$ knots (102 m/s)<br />- Exit Mach number: $M_7 = 1$<br />- Turbine exit temperature: $T_{t,7} = 1580^\circ F$ (860°C)<br /><br />(a) Effective exhaust velocity:<br /><br />The effective exhaust velocity ($v_{eff}$) can be calculated using the following formula:<br /><br />$v_{eff} = \sqrt{\frac{2 \cdot \gamma \cdot R \cdot T_{t,7}}{M_7^2}}$<br /><br />Where:<br />- $\gamma$ is the specific heat ratio (for air, $\gamma \approx 1.4$)<br />- $R$ is the specific gas constant (for air, $R \approx 287$ J/(kg·K))<br />- $T_{t,7}$ is the turbine exit temperature in Kelvin<br />- $M_7$ is the exit Mach number<br /><br />Substituting the values:<br /><br />$v_{eff} = \sqrt{\frac{2 \cdot 1.4 \cdot 287 \cdot (860 + 273.15)}{1^2}}$<br /><br />$v_{eff} \approx 1,000$ m/s<br /><br />(b) Net thrust:<br /><br />The net thrust ($F_{net}$) can be calculated using the following formula:<br /><br />$F_{net} = \dot{m} \cdot (v_{eff} - v_{t-0})$<br /><br />Where:<br />- $\dot{m}$ is the mass flow rate of the exhaust gases<br />- $v_{eff}$ is the effective exhaust velocity<br />- $v_{t-0}$ is the flight speed<br /><br />To find the mass flow rate ($\dot{m}$), we can use the following formula:<br /><br />$\dot{m} = \frac{F_g}{v_{t-0}}$<br /><br />Substituting the values:<br /><br />$\dot{m} = \frac{34,000}{102} \approx 333.33$ kg/s<br /><br />Now, we can calculate the net thrust:<br /><br />$F_{net} = 333.33 \cdot (1,000 - 102) \approx 327,830$ N or 32.78 kN<br /><br />Therefore, the effective exhaust velocity is approximately 1,000 m/s, and the net thrust is approximately 32.78 kN.