EXAMPLE $3$: A fluid mixer has the flow diagram shown in the figure. The flow is steady and

horizontal. There is a heat leak out of the system of $4\mathrm{.}65k\frac{J}{k}g$ of steam $C.$ The enthalpies

of streams are $h_A=15\mathrm{.}12k\frac{J}{k}g,h_B=227\mathrm{.}95k\frac{J}{k}g$ and $h_C=214k\frac{J}{k}g.$ If stream C

flows at the rate of $0\mathrm{.}45k\frac{g}{s},$ what are the flow rates of streams A and B$?$ Assume that

changes in the kinetic energy are negligible.

$0={\displaystyle \underset{\text{a}\text{l}\text{l}\text{f}\text{l}\text{o}\text{w}\text{s}in}{\overset{?}{}}}{h}_{in}d{m}_{in}-{\displaystyle \underset{\text{a}\text{l}\text{l}\text{f}\text{l}\text{o}\text{w}\text{s}\text{o}\text{u}\text{t}}{\overset{?}{}}}{h}_{\text{o}\text{u}\text{t}}d{m}_{\text{o}\text{u}\text{t}}+dQ$