PROBLEM $3-$ A $0\mathrm{.}25ft$ diameter circular cylinder spans a $3ft$ wide, rectangular open channel as shown below.

The flow rate is $2cfs.$ The temperature is $70F$ and the bottom of the channel is flat $($not sloped$).$

$(3\mathrm{.}1)$ Estimate the drag force and direction from the water onto the cylinder.

$(3\mathrm{.}2)$ Estimate the drag force and direction from the cylinder onto the water.

$(3\mathrm{.}3)$ Will the water depth downstream of the cylinder increase or decrease due to this drag force? Explain.

$(3\mathrm{.}4)$ Apply the conservation of linear momentum $($forces $=$ fluxes$)$ to a control volume that goes from the

upstream depth $(0\mathrm{.}8ft)$ to the location shown just downstream of the channel. What is the depth of the

downstream location?

Hint: the pressure force is still the pressure at the surface centroid times the area!