The Problem:

a$.$ To find the head loss between locations $\backslash (\backslash$mathbf$\{1\backslash$& $2\}\backslash )$ as labelled in the diagram, which of the conservation equations should be used?

b$.$ Draw the necessary diagram and solve for the head loss between locations $\backslash (1\backslash$& $2\backslash ).$ Explicitly state all assumptions.

Note:

$-$ Locations $1\backslash$&$2$ are open to air and have negligible velocity.

$\backslash (-1\backslash$mathrm$\{$hp$\}=550\backslash$mathrm$\{$ft$\}\backslash$mathrm$\{$lbf$\}/\backslash$mathrm$\{$s$\}\backslash ).$

c$.$ The head loss between locations $\backslash (2\backslash$& $3\backslash )$ is $10$ ft $.$ What is the $1$D uniform speed at location $3?$ Show the necessary diagram and explicitly state all assumptions.