Question $2($P$10-48,$ Mott, $2006)(25$ marks$)$

The adjacent figure shows a test setup for determining

the energy loss due to a heat exchanger. Water is used

as the test fluid and flows at $0\mathrm{.}006\frac{m^3}{s}$ upward

through the heat exchanger.

$($a$)$ Calculate the frictional head loss between

points $(1)$ and $(2),$ in meters of water.

$($b$)$ If the straight pipe friction losses between

$(1)$ and $(2)$ are $0\mathrm{.}1\frac{J}{k}g,$ what are the losses

associated with the flow through the

exchanger?

$($c$)$ If the frictional head loss through the heat

exchanger can be represented as $h_{L(ex)}=$

$K\frac{V^2}{2}g($where $V$ is the velocity in the inlet

pipe$),$ find the loss coefficient $\text{'}K\text{'}$ for the

heat exchanger.