Correct Answer - Option 3 : Will remain constant till a point and then gradually decrease
Concept:
Given:
Back pressure, Pb = 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.