Question

Water at 65 oF and 20 psia is heated in a chamber by mixing it with saturated water vapor at 20 psia. If both streams enter the mixing chamber at the same mass flow rate, determine the temperature and the quality of the exiting stream.

Answer 1

Explanation:

Equation for mass balance is as follows.

        $\Delta m_{system} = m_{in} - m_{out} = 0$

          $m_{in} = m_{out}$

    $m_{1} + m_{2} = m_{3} = 2m$ .......... (1)

            $m_{1} = m_{2} = m$

Equation for energy balance is as follows.

       $E_{in} - E_{out} = \Delta E = 0$

              $E_{in} = E_{out}$

Hence,      $m_{1}h_{1} + m_{2}h_{2} = m_{3}h_{3}$ ......... (2)

When we combine both equations (1) an d(2) will be as follows.

          $m_{1}h_{1} + m_{2}h_{2} = 2mh_{3}$

or,       $h_{3} = \frac{(h_{1} + h_{2})}{2}$

Hence, putting the given values into the above equation as follows.

              $h_{3} = \frac{(h_{1} + h_{2})}{2}$

            $h_{3} = \frac{(33.08 + 1156.2)}{2}$

                            = 594.6 Btu/lbm

Therefore,      $T_{3} = T_{sat 20psi} = 228^{o}F$

And,       $x_{3} = \frac{h_{3} - h_{f}}{h_{fg}}$

                           = $\frac{594.6 - 196.27}{1156.2 - 196.27}$

                           = 0.415