A stream of superheated steam ( $2 \mathrm{MPa}, \: 300^{\circ} \mathrm{C}$) mixes with another stream of superheated steam $\left(2 \mathrm{MPa}, \: 400^{\circ} \mathrm{C}\right)$ through a steady-state adiabatic process. The flow rates of the streams are $3 \mathrm{~kg} / \mathrm{min}$ and $2 \mathrm{~kg} / \mathrm{min}$, respectively. This mixture then expands in an adiabatic nozzle to a saturated mixture with quality of $0.77$ and $1\: \mathrm{kPa}$. Neglect the velocity at the nozzle entrance and the change in potential energies. The velocity at the nozzle exit (in $\mathrm{m} / \mathrm{s}$ ) is $\_\_\_\_\_\_\_$ (rounded off to two decimal places).
Use the following data:
At $2 \: \mathrm{MPa}, \: 300^{\circ} \mathrm{C}$ : Specific enthalpy of superheated steam $=3024.2 \mathrm{~kJ} / \mathrm{kg}$
At $2 \mathrm{MPa}, 400^{\circ} \mathrm{C}$ : Specific enthalpy of superheated steam $=3248.4 \mathrm{~kJ} / \mathrm{kg}$
At $1 \: \mathrm{kPa}$ : Specific enthalpy of saturated water $=29.3 \mathrm{~kJ} / \mathrm{kg}$
At $1 \: \mathrm{kPa}$ : Specific enthalpy of saturated vapour $=2513.7 \mathrm{~kJ} / \mathrm{kg}$
