Exhaust Velocity Given Gross Thrust In Turbojet Calculator

Formula Used:

\[ V_e = \frac{T_G - (p_e - p_{\infty}) \times A_e}{\dot{m}_a \times (1 + f)} \]

Gross Thrust of Turbojet (T_G):

Nozzle Exit Pressure (p_e):

Ambient Pressure (p_∞):

Nozzle Exit Area (A_e):

m²

Mass Flow Rate Turbojet (ṁ_a):

kg/s

Fuel Air Ratio (f):

Exit Velocity (V_e):

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1. What is Exhaust Velocity in Turbojet Engines?

Exit Velocity refers to the speed at which gases expand at the exit of nozzle of a turbojet engine. It is a critical parameter that directly affects the thrust produced by the engine and overall engine performance.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V_e = \frac{T_G - (p_e - p_{\infty}) \times A_e}{\dot{m}_a \times (1 + f)} \]

Where:

\( V_e \) — Exit Velocity (m/s)
\( T_G \) — Gross Thrust of Turbojet (N)
\( p_e \) — Nozzle Exit Pressure (Pa)
\( p_{\infty} \) — Ambient Pressure (Pa)
\( A_e \) — Nozzle Exit Area (m²)
\( \dot{m}_a \) — Mass Flow Rate Turbojet (kg/s)
\( f \) — Fuel Air Ratio

Explanation: The formula calculates the exhaust velocity by considering the gross thrust, pressure difference at nozzle exit, nozzle area, mass flow rate, and fuel-air mixture ratio.

3. Importance of Exhaust Velocity Calculation

Details: Accurate exhaust velocity calculation is crucial for determining engine efficiency, thrust optimization, and overall performance analysis of turbojet engines. It helps engineers design more efficient propulsion systems and predict engine behavior under various operating conditions.

4. Using the Calculator

Tips: Enter all values in appropriate units (N for thrust, Pa for pressure, m² for area, kg/s for mass flow rate). Ensure all values are positive and physically meaningful for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: Why is exhaust velocity important in turbojet engines?
A: Exhaust velocity directly determines the thrust produced by the engine and affects fuel efficiency, making it a critical performance parameter.

Q2: What are typical exhaust velocity values for turbojet engines?
A: Typical exhaust velocities range from 400-800 m/s for subsonic engines and can exceed 1000 m/s for high-performance military and supersonic engines.

Q3: How does ambient pressure affect exhaust velocity?
A: Higher ambient pressure reduces the effective pressure difference at the nozzle exit, which can decrease exhaust velocity and thrust output.

Q4: What is the significance of fuel-air ratio in this calculation?
A: The fuel-air ratio accounts for the additional mass flow from fuel injection, which affects the total mass flow rate through the engine.

Q5: Are there limitations to this calculation method?
A: This calculation assumes ideal gas behavior and may not account for complex flow phenomena, real gas effects, or varying specific heat ratios in actual engine operations.