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Consider the following statements in relation to a convergent divergent steam nozzle operating under choked conditions:  
1. In the convergent portion steam velocity is less than sonic velocity
2. In the convergent portion steam velocity is greater than sonicvelocity
3. In the divergent portion the steam velocity is less them sonicvelocity
4. In the divergent portion the steam velocity is greater than sonicvelocity
Which of the above statements are correct?
  • a)
    1 and 3
  • b)
    1 and 4
  • c)
    2 and 3
  • d)
    2 and 4
Correct answer is option 'B'. Can you explain this answer?
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Convergent-Divergent Steam Nozzle operating under choked conditions

In a convergent-divergent steam nozzle, the steam passes through a converging section followed by a diverging section. When the nozzle is operating under choked conditions, the flow velocity reaches the local sonic velocity. Let's analyze the given statements:

Statement 1: In the convergent portion, steam velocity is less than sonic velocity.
This statement is incorrect. In the convergent portion of the nozzle, as the cross-sectional area decreases, the steam velocity increases. Eventually, it reaches the local sonic velocity at the throat.

Statement 2: In the convergent portion, steam velocity is greater than sonic velocity.
This statement is correct. As mentioned above, the steam velocity in the convergent portion increases and becomes equal to the local sonic velocity at the throat.

Statement 3: In the divergent portion, the steam velocity is less than sonic velocity.
This statement is incorrect. In the divergent portion of the nozzle, the steam expands and accelerates further, resulting in a steam velocity greater than the sonic velocity.

Statement 4: In the divergent portion, the steam velocity is greater than sonic velocity.
This statement is correct. As the steam expands in the divergent portion, the velocity increases and can exceed the sonic velocity.

Explanation:
- The convergent section of the nozzle is designed to accelerate the steam and increase its velocity by decreasing the cross-sectional area.
- At the throat of the nozzle, where the cross-sectional area is the smallest, the steam velocity reaches the local sonic velocity. This is the point of maximum acceleration.
- In the divergent section, the steam expands and its velocity continues to increase. This is due to the conversion of pressure energy into kinetic energy.
- If the nozzle is operating under choked conditions, the steam velocity remains at the local sonic velocity throughout the throat and divergent section.
- The divergent section allows the steam to expand and convert its high-pressure energy into kinetic energy, resulting in a high-velocity jet at the nozzle exit.

Therefore, the correct statements are:
- In the convergent portion, steam velocity is greater than sonic velocity.
- In the divergent portion, the steam velocity is greater than sonic velocity.
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Consider the following statements in relation to a convergent divergent steam nozzle operating under choked conditions:1. In the convergent portion steam velocity is less than sonic velocity2. In the convergent portion steam velocity is greater than sonicvelocity3. In the divergent portion the steam velocity is less them sonicvelocity4. In the divergent portion the steam velocity is greater than sonicvelocityWhich of the above statements are correct?a)1 and 3b)1 and 4c)2 and 3d)2 and 4Correct answer is option 'B'. Can you explain this answer?
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