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Statement (I) : Mass flow through the convergent nozzle is maximum when the exit Mach number is 1. Statement (II) : The divergent section is added to convergent nozzle to increase the exit Mach number and not to increase the mass flow rate

Statement (I) : Mass flow through the convergent nozzle is maximum when the exit Mach number is 1. Statement (II) : The divergent section is added to convergent nozzle to increase the exit Mach number and not to increase the mass flow rate Correct Answer Both Statement (I) and Statement (II) are individually true but Statement (II) is NOT the correct explanation of Statement (I)

Concept:

A nozzle is a passage of smoothly varying cross-section by means of which the pressure energy of working fluid is converted into kinetic energy.

  • A nozzle whose flow area decreases in the flow direction is called a Convergent nozzle.
  • It is designed such that a drop in pressure from inlet to outlet accelerates the flow. 
  • The location of the smallest flow area of a nozzle is called the throat.
  • The ratio of the pressure at the section where sonic velocity is attained to the inlet pressure of a nozzle is called the critical pressure ratio.
  • It happens at Mach number equals 1.

Mach number < 1 → subsonic velocity

Mach number = 1 → sonic velocity

Mach number > 1 → supersonic velocity

  • If a convergent nozzle is operating under choked condition, the exit Mach number is unity.
  • To determine whether a nozzle is choked or not, we calculate the actual pressure ratio and then compare this with the critical pressure ratio.
  • If the actual pressure ratio > critical pressure ratio, the nozzle is said to be choked.

Convergent-divergent nozzle:

  • Convergent - Divergent nozzles are used to increase the flow of gas to supersonic speeds (as in the case of rockets).
  • Their cross-sectional area first decreases and then increases. The area where the diameter is minimum is called the throat.
  • As the gas enters the converging section, its velocity increases, considering the mass flow rate to be constant.
  • As the gas passes through the throat, it attains sonic velocity (Mach number = 1).
  • As the gas passes through the divergent nozzle, the velocity increases to supersonic (Mach number >1)
  • The flow rate is maximum for a given nozzle if the flow is sonic at the throat. This condition is achieved by managing the back pressure.
  • For the compressible fluid flow, the Mach number is an important dimensionless parameter. On the basis of the Mach number, the flow is defined.
  • The addition of divergent to convergent does not alter the mass flow rate as the flow is choked.

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