West Palm Beach has some very specific municipal codes pertaining to any exterior projects. Your best bet is to first call the Palm Beach building dept. or visit their offices and get the current codes pertaining to a privacy fence. Things like "in concrete" and "post spacing" will not be code issues and will depend upon what you are choosing for fencing material. The building dept. or plan and zone will have specific information on height and certain fencing material that is not acceptable. Further it will be very important that you are quite clear on exactly where you lot line is. Unless there is something that clearly identifies the lot lines you may need to call in a surveyor. This wouldn't be much of a big deal or cost since they can now do this with GPS equipment.
Dennis (cut2it)
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C&onstructi&on C&onsultant
Over 40 yrs. as General Contractor for new const. & remodel - retired with time for you.