Question

If a rocket engine produces 30 kN thrust operating at chamber pressure of 4 MPa with throat diameter of 100 mm, then the thrust coefficient of a rocket engine is:

• A. 0.96
• B. 0.85
• C. 0.92
• D. 0.94

Hint:

Thrust coefficient relates actual thrust to chamber pressure and throat area—it indicates nozzle performance.

Answer 1

The Correct Option is A

The thrust coefficient (C_F) of a rocket engine can be determined using the formula:

C_F = \(\frac{T}{P_c \cdot A_t}\) 

Where:

• T = Thrust produced by the rocket engine (30 kN = 30000 N)
• P_c = Chamber pressure (4 MPa = 4000000 Pa)
• A_t = Throat area

To find A_t, we use the formula for the area of a circle:

A_t = \(\pi \cdot (\frac{d}{2})^2\)

Given:

• Throat diameter d = 100 mm = 0.1 m

Calculate A_t:

A_t = \(\pi \cdot (0.05)^2 = \pi \cdot 0.0025 = 0.00785\) m²

Now, insert the values into the thrust coefficient formula:

C_F = \(\frac{30000}{4000000 \cdot 0.00785}\)

C_F = \(\frac{30000}{31400}\)

C_F ≈ 0.9554

The calculated thrust coefficient, rounded to two decimal places, is 0.96. Therefore, the correct answer is 0.96.