Mortimer Schnerd, RN wrote:
If I were trying to stretch a flight and even then only if I were alone, I might
consider running one dry. But I have to tell you: running a tank dry in a
Cherokee results in te longest 30 seconds of your life.

Four tank Pipers (PA28-235, PA32-300 series) manuals specifically state
that up to 10 seconds is required for fuel to refill the system after
running an outboard tank dry.

1972 PA32-300 POH, page 4-1, Emergency Procedures, Engine Powere Loss
During Takeoff and page 4-2, Engine Powere Loss in Flight
and
1979 PA32-300 POH, page 3-7, Emergency Procedures, Section 3.9, Engine
Powere Loss During Takeoff and page 3-8,Section 3.11, Engine Powere Loss
in Flight

"NOTE: If an engine failure was caused by fuel exhaustion, power will
not be regained after tanks are switched until empty fuel lines are
filled, which may require up to ten seconds."