I'm assuming here that we are talking about a flue pipe, which is a
non-reed or horn pipe.

The part that conducts the wind from the chest to the pipe is called
the foot.  One side of the foot is planted in the wind chest, the other
end of the pipe is in the block (or some call it the throat).  Some
blocks are cut so as to direct the wind coming from the foot against
the upper lip of the pipe.  Some other blocks, like in the Reproduco
flutes, have just a wind channel that conducts the wind at right angles
to the cap.  The part of the pipe directly below the square hole in the
front of the pipe is called the cap.  Some caps are cut in such a way
(as in the Reproduco) as to direct the wind coming from the block to
the upper lip.  The upper lip is the thin lower part of the chamfered
front that forms the upper part of the square mouth.  The part of the
pipe the wind comes out of to sound the pipe is called the windway.
This is a thin slit formed by the back of the cap and the front of the
block.  The front of the pipe has a hole called the mouth of the pipe.
The fronts of wooden pipes are chamfered at an angle either on the
outer surface of the pipe or on the inside of the pipe.  These latter
pipes present a flat front to the viewer.

Some flutes have a lead piece that rolls across the top for tuning.
This is called oddly enough the tuner or tuning scroll.  Some other
flutes have a slot that has a metal tuning slide that moves up or down
to tune the pipe by changing the effective length of the pipe.  Still
other types of flutes have a stopper, a piece of wood with a handle
that fits into the top of the pipe, that can be moved up or down to
tune the pipe.  These are called "stopped" pipes.

These names for pipe parts seem to be in general use in America.  Brits
might have other names for them.  Hope this helps.

Tony Marsico
Pittsburgh, Pa.