In this problem, we are given the conditions of superheated steam passing through a convergent-divergent nozzle. We are required to find the exit pressure at which the steam mass flow rate will remain fixed. The critical pressure ratio is given as 0.55.



The mass flow rate of steam passing through the nozzle can be expressed as:

$\dot{m} = \rho A V$

where,
$\dot{m}$ = mass flow rate
$\rho$ = density of steam
$A$ = cross-sectional area of the nozzle
$V$ = velocity of steam

From the continuity equation, we know that the mass flow rate remains constant throughout the nozzle. Therefore, we can write:

$\rho_{1} A_{1} V_{1} = \rho_{2} A_{2} V_{2}$

where,
$\rho_{1}$ and $V_{1}$ are the density and velocity of steam at the inlet of the nozzle, and
$\rho_{2}$ and $V_{2}$ are the density and velocity of steam at the exit of the nozzle.

We also know that the pressure variation across the nozzle is governed by the Bernoulli's equation:

$P_{1} + \frac{1}{2}\rho_{1} V_{1}^{2} = P_{2} + \frac{1}{2}\rho_{2} V_{2}^{2}$

where,
$P_{1}$ and $P_{2}$ are the pressure at the inlet and exit of the nozzle.

At the critical pressure ratio, the exit pressure is given by:

$P_{2} = P_{1} \times \left(\frac{2}{2.4}\right)^{\frac{2.4}{1.4}}$

$P_{2} = 0.517 \times P_{1}$

Therefore, the exit pressure at which the steam mass flow rate will remain fixed is 51.7 kg/cm^(2).



In conclusion, we can say that by using the continuity equation and Bernoulli's equation, we were able to determine the exit pressure at which the steam mass flow rate will remain fixed. The critical pressure ratio of 0.55 was used to calculate the exit pressure.