Question

For supersonic O\(_2\) jet in basic oxygen furnace steelmaking, choose the correct combination from the following:
(1) Converging-diverging nozzle
(2) Diverging-converging nozzle
(3) O\(_2\) velocity greater than sound velocity at nozzle throat (Mach number > 1)
(4) O\(_2\) velocity equal to sound velocity at nozzle throat (Mach number = 1)
(5) Exit O\(_2\) jet pressure \(\ge\) atmospheric pressure
(6) Exit O\(_2\) jet pressure \(<\) atmospheric pressure

• A. (1), (4), (5)
• B. (1), (3), (6)
• C. (2), (3), (5)
• D. (2), (4), (5)

Hint:

For accelerating gas to supersonic speeds, remember the sequence: 1. {Shape:} Converging-Diverging (CD) nozzle. 2. {Throat:} Mach = 1 (sonic). 3. {Exit:} Mach>1 (supersonic). This is a fundamental concept in gas dynamics and rocket propulsion.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This question concerns the principles of compressible fluid flow as applied to the oxygen lance in a Basic Oxygen Furnace (BOF). The goal is to create a supersonic jet of oxygen to refine molten iron into steel.
Step 2: Detailed Analysis of Each Statement:
- Nozzle Type (1 vs 2): To accelerate a gas from subsonic to supersonic speeds, a specific nozzle geometry is required. The gas first accelerates in a converging section, reaching the speed of sound (Mach 1) at the narrowest point, called the throat. To accelerate further to supersonic speeds (Mach>1), the gas must then expand through a diverging section. This specific geometry is called a converging-diverging (CD) nozzle or a de Laval nozzle. Therefore, statement (1) is correct and (2) is incorrect.
- Throat Velocity (3 vs 4): According to the theory of compressible flow, the maximum velocity that can be achieved in a purely converging nozzle is Mach 1 at the exit. To go supersonic, the flow must pass through a throat where the velocity is sonic. Therefore, the velocity at the nozzle throat is equal to the speed of sound (Mach number = 1). Statement (4) is correct and (3) is incorrect. The supersonic velocity (Mach>1) is achieved *after* the throat, in the diverging section.
- Exit Pressure (5 vs 6): The purpose of the supersonic oxygen jet is to penetrate the slag layer and react with the molten metal bath. To do this effectively, the jet must have sufficient momentum and must not be immediately dissipated by the furnace atmosphere. The jet is designed to be either "correctly expanded" (exit pressure = atmospheric pressure) or, more commonly, "underexpanded" (exit pressure>atmospheric pressure). An underexpanded jet continues to expand and accelerate outside the nozzle, which can be beneficial for the process. A jet with exit pressure less than atmospheric ("overexpanded") would be unstable and inefficient. Therefore, the exit pressure must be greater than or equal to the atmospheric pressure inside the furnace. Statement (5) is correct and (6) is incorrect.
Step 3: Combining the Correct Statements:
The correct statements are (1), (4), and (5). This combination corresponds to option (A).
Step 4: Why This is Correct:
The design and operation of a supersonic oxygen lance are based on well-established principles of gas dynamics: a CD nozzle is required to achieve supersonic flow, the throat condition is always sonic (Mach 1), and the jet is designed to be underexpanded for process efficiency. Option (A) correctly combines these three principles.