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Gaseous Nitrogen at 30°C is expanded through a converging nozzle from a total pressure of 0.5 MPa to a back pressure chamber. If the back pressure is increased from 0.1 MPa to 0.4 MPa in steps of 0.02 MPa, the trend in mass flow rate through the nozzle
1. Will gradually decrease
2. Will gradually increase
3. Will remain constant till a point and then gradually decrease
4. Will remain constant till a point and then gradually increase

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Correct Answer - Option 3 : Will remain constant till a point and then gradually decrease

Concept:

Given:

Back pressure, P= 0.5 MPa, Adiabatic index, \(\gamma = 1.4\)

For expansion process, critical pressure ratio

\(\frac{{{{\rm{P}}_{\rm{c}}}}}{{{{\rm{P}}_{\rm{b}}}}} = {\left[ {\frac{2}{{{\rm{\gamma }}\;+\;1}}} \right]^{\frac{{\rm{\gamma }}}{{\left( {{\rm{\gamma }}\;-\;1} \right)}}}}\)

\(\frac{{{{\rm{P}}_{\rm{c}}}}}{{0.5}} = {\left[ {\frac{2}{{1.4\; + \;1}}} \right]^{\frac{{1.4}}{{\left( {1.4\; -\; 1} \right)}}}}\)

∴ Pc = 0.264 MPa

Critical pressure, Pc = 0.264 MPa

So, when the pressure is increased from 0.1 MPa to the critical pressure, the mass flow rate remains constant but after increasing beyond critical pressure, mass flow rate decreases.

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