$(10\%)$ Using the flow system shown here and applying the large tank approximation, discuss the concepts of the Energy line and the Hydraulic Grade Line. Apply Bernoulli Equation to analyze the flow system at points $1,2,$&$3$ to express an equation for the total energy $H$ at each point. Assume ideal conditions. Your diagram must be neatly presented and fully labeled. The lines must be neatly drawn.

$(10\%)$ Air flows to a stationary rectangular board with a certain upstream velocity $V_0$ and pressure po$.$ Using a neatly sketched and well$-$labeled diagram of the flow streamlines incident on the board, discuss the concepts of the stagnation point and the stagnation pressure. Apply Bernoulli equation to the system to develop the relevant equation applicable to the system.

$(30\%)$ With the aid of a well$-$labeled and neatly sketched control volume, apply the Reynolds Transport Theorem to obtain the following governing equations in their basic forms: Provide a step$-$by$-$step derivation and state the reason$($s$)$ for the elimination of any term or variable. No jumps!

$3($a$)(10\%)$ The conservation of mass equation for a fixed, non$-$deforming control volume.

$3($b$)(10\%)$ The equation of linear momentum for a fixed, non$-$deforming control volume.

$3($c$)(10\%)$ The conservation of energy equation for a fixed, non$-$deforming control volume.