# External Fluid Flow -- Immersed Body Friction Drag

1. Nov 30, 2016

### 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. The problem statement, all variables and given/known data

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.

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

DF=(1/2)*ρ*∪2*b*L*CDf

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.

3. 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 CDf term

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

2. Nov 30, 2016

### haruspex

3. Nov 30, 2016

### Nidum

Pdf

4. Nov 30, 2016

### pistolpete

That value for Cd 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 CDf not Cd I believe.

5. Nov 30, 2016

### pistolpete

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 CD 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?