External Fluid Flow -- Immersed Body Friction Drag

[pistolpete]

Hello all, I have browsed this forum occasionally when I had questions and threads showed up on a search. I have been stumped by a problem, so I decided to create an account and see if anyone could help me out!

1. Homework Statement
A coal barge 1000 ft long and 100 ft wide is submerged in a depth of 12 ft in 60°F Water. It is being towed at a speed of 12 mph. Estimate the friction drag on the barge.

Homework Equations

When treating the submerged part of the barge as Flat plate the equation for Drag Friction is :

D_F=(1/2)*ρ*∪²*b*L*C_Df

Since the submerged part of the barge would have three "faces" that are parallel to the flow direction (2 side faces of 1000ft*12ft, and one bottom face of 100ft*1000ft) would I add up the total area of the submerged faces parallel to the flow to use in the above equation?

The only examples I can find have only the bottom part of the plate, but they are floating so that seems logical to me.

The Attempt at a Solution

Converted the 12 mph to ft/s then Calculated Reynolds # to find laminar/turb regions and use appropriate eqns to Find the C_Df term

Using found values and properties of water @ 60°F solve for D_F

 

[haruspex]

Certainly you should include the area along the sides, but what about front and back?
Searching online I found two places that quote C_d=2.1 for a rectangular box, but neither makes it clear what area to use. E.g.
http://www.engineeringtoolbox.com/drag-coefficient-d_627.html

 

[Nidum]

Pdf

 

[pistolpete]

That value for C_d would work to find the total drag force (due to skin friction and pressure drag), but this question asks just for the friction drag and the drag coefficient that would need to be used (or assumed and then iterated with Renolds # until convergence) is C_Df not C_d I believe.

 

[pistolpete]

Pdf

Thanks for that, that makes thing a bit more clear! From that I see the area is selected depending on the application and in the case of the barge it implies that you would use wetted area (all submerged faces in th fluid) which would include the front and back faces (the two faces normal to the direction of flow). It makes sense to me to use this area if you were using a value of C_D and finding the total drag.

Since friction drag is due to the shear at the wall, and these faces are normal to the direction of flow (cant support shear in the direction of drag force) so am I right in saying these faces should not be included in the Area when finding the frictional drag only?