Question

A chemical rocket with an ideally expanded flow through the nozzle produces $5 \times 10^6$ N thrust at sea level. The specific impulse of the rocket is $200$ s and acceleration due to gravity at sea level is $9.8$ m/s$^2$. The propellant mass flow rate out of the rocket nozzle is .............. kg/s (rounded off to the nearest integer).

Hint:

Always remember: thrust from a rocket is directly proportional to the product of propellant mass flow and exhaust velocity. Using $I_{sp} g_0$ as effective exhaust velocity simplifies the calculation.

Answer 1

Step 1: Formula for thrust.
For a rocket under ideally expanded nozzle conditions:
\[ T = \dot{m} \, I_{sp} \, g_0 \]
where  
\[ T = \text{thrust} = 5 \times 10^6 \, \text{N} \]
\[ I_{sp} = \text{specific impulse} = 200 \, \text{s} \]
\[ g_0 = \text{standard gravity} = 9.8 \, \text{m/s}^2  \]
 

Step 2: Rearranging for \(\dot{m}\): 
\[ \dot{m} = \frac{T}{I_{sp} \, g_0} \]
\[ \dot{m} = \frac{5 \times 10^6}{200 \times 9.8} \]
\[ \dot{m} = \frac{5 \times 10^6}{1960} \approx 2551 \, \text{kg/s}\]
\[ \boxed{2551 \, \text{kg/s}} \]