Exhaust Velocity Calculator

Historical Background

The concept of exhaust velocity originated with the study of rocket propulsion in the early 20th century. Konstantin Tsiolkovsky, Robert Goddard, and Hermann Oberth made significant contributions, laying the groundwork for modern rocketry. Exhaust velocity is fundamental in determining the efficiency of rocket engines and is a critical parameter in the Tsiolkovsky rocket equation.

Formula

The exhaust velocity formula is:

\[ V = \frac{F - (p_e - p_a) \cdot A}{\dot{m}} \]

where:

• \( V \) is the exhaust velocity (m/s),
• \( F \) is the thrust force (N),
• \( p_e \) is the exit pressure (N/m²),
• \( p_a \) is the atmospheric pressure (N/m²),
• \( A \) is the exhaust area (m²),
• \( \dot{m} \) is the mass flow rate (kg/s).

Example Calculation

Suppose a rocket engine generates a thrust of 50,000 N, with an exit pressure of 120,000 N/m², an atmospheric pressure of 101,325 N/m², an exhaust area of 1.2 m², and a mass flow rate of 45 kg/s. The exhaust velocity is calculated as follows:

\[ V = \frac{50000 - (120000 - 101325) \cdot 1.2}{45} \approx 831.25 \, \text{m/s} \]

Common FAQs

What is exhaust velocity in rocket science?

• It refers to the linear flow rate of exhaust gases exiting a rocket, determining the thrust and efficiency of the engine.

Why is exhaust velocity important?

• Higher exhaust velocities contribute to more efficient rockets, resulting in greater thrust per unit of fuel consumed.

Does atmospheric pressure affect exhaust velocity?

• Yes, the difference between exit and atmospheric pressures influences the thrust and, consequently, the exhaust velocity.