This method may serve a single vessel. If you want to know the power for a tug to handle a group of barges connected in x and y directions, it is best to check on some barge group testing data. You may also try to make estimation with this approach. Wide body barges are considered streamline in buttock flow.
Some barges have slight fairing in spoon bow to ease the flow at the waterline.
For flat swim front and ends, you may apply calculation as impact on inclined surfaces. Don't forget to add varies allowance for directional skegs, with intentional drag, and also loses due to lock-in stern waterline flow. Add allowance for barges without effective bow corner flow fairing. There don't seem to be any equations or imperical data for this type of vessel. Please email if you have any information.