Problem $2.$ The flow in a diamond$-$shaped conduit transitions from open channel to pressure

flow. The conduit is horizontal and the water depth just upstream of the transition is $2$ ft $.$

The conduit is completely full downstream. Pressure gage readings are as shown.

a$.$ Calculate the pressure forces upstream and downstream.

b$.$ Determine $V_1$ and $V_2$ with respect to the flow rate $Q.$

c$.$ Using linear momentum, calculate the flow rate $Q.$

$($a$)$

$($b$)$