Question

The critical mass flow rate through a converging-diverging nozzle

• A. is inversely proportional to stagnation speed of sound
• B. is directly proportional to stagnation speed of sound
• C. is directly proportional to stagnation temperature
• D. is inversely proportional to stagnation pressure

Hint:

In applications where control over the mass flow rate is needed, manipulating the stagnation temperature can be an effective method.

Answer 1

The Correct Option is C

Step 1: Understanding Critical Conditions in Nozzles.
The critical mass flow rate through a converging-diverging nozzle is achieved when the flow reaches sonic conditions at the throat of the nozzle.
Step 2: Relation to Stagnation Conditions.
According to the gas dynamics fundamental equations, the mass flow rate (\(\dot{m}\)) for an ideal gas through a critical section is given by: The mass flow rate \(\dot{m}\) is given by the formula: \[ \dot{m} = \frac{\rho_0 A}{\sqrt{T_0}} \sqrt{\frac{\gamma}{R}} \] where \(\rho_0\) is the stagnation pressure, \(T_0\) is the stagnation temperature, \(\gamma\) is the specific heat ratio, \(R\) is the gas constant, and \(A\) is the throat area. This equation shows that the mass flow rate is directly proportional to the square root of the stagnation temperature.