$5.)$ In the system shown below, assume that major head loss in the pipe is given by the equation:

$\backslash [$

h$\_\{$L$\}=0\mathrm{.}014\backslash$frac$\{$L$\}\{$D$\}\backslash$frac$\{$v$^\{2\}\}\{2$ g$\}$

$\backslash ]$

where $\backslash ($ L $\backslash )$ is the length of pipe and $\backslash ($ D $\backslash )$ is the diameter. Neglect any minor losses at the pipe entrance in the bottom of the tank on the left. Hint: Note that this system appears very similar to one of our examples in class, but the different nozzle at the end $($with a different diameter$)$ will change things.

a$.)$ Find a relationship between the velocity in the pipe and the velocity exiting the nozzle, noting that the pipe and nozzle opening have different diameters. Express

the relationship as an equation for calculating velocity in the nozzle as a function of the velocity in the pipe. $(5$ points$)$

b$.)$ Determine the discharge of water through this system. Hints: Apply the energy equation at the two points where you know the most information about the flow characteristics $($pressure$,$ elevation, velocity$).$ Also note that the head loss equation given above corresponds to the flow in the pipe. You will need to incorporate the relationship you developed in part a$.(5$ points$)$

c$.)$ Sketch the HGL and EGL for this system. Hint: Note that the nozzle's change in diameter will change the relationship between the HGL and EGL, as compared with the rest of the pipe. Accordingly, there will be some head remaining when the HGL and EGL reach the nozzle. $(5$ points$)$

d$.)$ Determine the height of the EGL above the entrance to the nozzle. What does this suggest regarding the location of maximum pressure in this system? Calculate the value of maximum pressure. Hint: Think about what will cause the EGL to change height between the tank and the nozzle. $(5$ points$)$

e$.)$ Locate the point of minimum pressure, and calculate its value. Do you expect cavitation to occur anywhere in the system? Assume atmospheric pressure is $101\mathrm{.}3$ kPa $,$ and the water is at $\backslash (10^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).(5$ points$)$