A storage tank carrying water is located on one side of a riverbank. The company that owns the storage

tank wants to build a pipeline that carries water from the storage tank to a reservoir located northeast on the

other side of the river bank. It would be easy to build the pipeline straight from the storage tank to the

reservoir, but it is more expensive to build diagonally across the river than it is to build on land and then

take the shortest river crossing. The company decided that the most optimal way to supply the water to the

reservoir is to build the pipeline going east along the river bank for $2$ miles. The pipeline will have a $45\backslash$deg

standard elbow and will travel northeast for $3$ miles until it fully crosses the river. The pipeline will then

have another $45\backslash$deg standard elbow that will travel north for $2$ miles until it reaches the reservoir. The material

used for the pipeline will be concrete with the highest pipe roughness, with a radius of $1\mathrm{.}5$ ft$.$ The

temperature outside remains at a temperature of $65\backslash$deg F$.$

Assume that the flow of water in the pipeline from the storage tank to the reservoir is at turbulent flow and

has a constant unknown velocity. Assume that the pressure inside the pipe is constant at $1$ atm. Assume you

have a $20$ hp pump.

$($a$)$ What is the Reynolds number of the water flow?

$($b$)$ What is the frictional loss of the entire system