Why would the water pressure from your well start out strong but drop quickly after opening the faucet?

Chances are the pipe is being constricted somewhere in the line. However, there is also a chance there is a problem with your well pump, water tank, or well itself.

It depends on what you mean by "quickly".

If the pressure is good right away, but almost seems to "spray" out of the faucet and then after just a few seconds drops to a low but stable pressure, then a constricted pipe is most likely the problem. If it is good right away, but then quickly drops after a 30 seconds, or minute or two, it could be a pipe but is more likely something wrong with the pump, tank, or well.

it occurs in only certain places in the house, then it is most likely a partial blockage in the pipe that leads to that specific faucet(s) or the faucet itself. If it is in the entire house, then it could be a partial blockage in the main line coming to the house or something to do with the pump, tank, or well.

A constricted pipe could be caused from pipe corrosion, foreign material, a bent area of pipe, a partially closed valve, or a partially frozen pipe. If you live in a cold climate and think freezing might be affecting the constricted areas in question then this might be the first thing to check by gently thawing the affected pipe areas as you would a frozen pipe to see if the pressure returns. Corroded pipes can be replaced or possibly cleaned with the water to that area turned off.

To see if it is the pump or related equipment , you can check the pressure at the pump or right after the water leaves the pump. This can be as easy as reading the gage on your pump or attaching a gage to a nearby hose bib or as hard as cutting out a piece of the pipe and installing a pressure gage directly in the line. You will have to determine if your pump already has a gage or a nearby hose bib to easily install a gauge or if you have access to somebody with the skills to do the pipe cutting. If the gauge shows a pressure drop after you open a faucet, you know to call in someone who services well pumps. If the gauge stays the same, you know the pipe is being partially blocked somewhere down the line. If you know it is the pump or other equipment, then there could be a million things possibly wrong with it from worn parts, to leaks, to a poor electrical supply. With research, you might be able to narrow down the problem and with the right resources you might be able to fix the pump yourself but calling in the pro will get you running water much faster and you wont have to deal with a potentially very deadly shock hazard!