The $30-$mm$-$diameter copper coil is used for a solar hot

water heater. Water at an average temperature of

$T=50C$ passes through the coil at $20$lite$\frac{r}{m}in.$ At

$50C$ the water has the density of $988k\frac{g}{m^3}$ and

kinematic viscosity of

$u=0\mathrm{.}561({10}^{-6})\frac{m^2}{s}.$ Take

$=0\mathrm{.}03mm$ for the coil. Suppose that $L=400mm.$

Use the equation

$\frac{1}{\sqrt[\phantom{2}]{f}}=-1\mathrm{.}8log[(\frac{\frac{}{D}}{3\mathrm{.}7}{)}^{1\mathrm{.}11}+\frac{6\mathrm{.}9}{Re}]*(Figure1)$

Figure

Determine the major head loss that occurs within the coil. Neglect the length of each

bend.

Express your answer to three significant figures and include the appropriate

units.

View Available Hint$($s$)$

Hint $1.$ How to approach the problem

Recall the Darcy$-$Weisbach equation for the major head loss and consider

the unknown quantities in it$.$ Use the given volumetric discharge to

determine the flow velocity. The friction factor can be obtained through the

given formula. Note: you can also use the Moody diagram to determine

the friction factor.

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