The water in the tank are pressurized to 50- 100 PSI? but water cannot be compressed I was looking up about how domestic water heater (DHW) works, and couldn't understand the following:
considering the fact that water (and all other liquids) cannot be compressed (practically), how can they state that the tank is a " heavy metal tank that holds 40 to 60 gallons (151 to 227 liters) of hot water at around 50 to 100 pounds per square inch (PSI), within the pressure range of a typical residential water system".
Do they mean that the water shoots out of the pipe at pressure of 50-100 PSI?
How can one pressurize water (or any other liquid) ? If I put a membrane in a sealed tank that separate the water from the air, and then I compress the air to lets say 50 PSI, then it can be said that the water are pressurized to 50 PSI? ( and that means that if I open a valve in water side of the tank, they'll shoot out at 50 PSI ? can you remind me how to find their velocity? it comes from bernoulli?)
 A: Pressure and compression are two different things. Pressure is pressure (force per area), while compression is a change in volume.
You can apply the same pressure to a balloon and a brick, and the balloon will compress much more than the brick. The pressure "inside" the balloon and brick will both end up being equal to the pressure, you apply from the outside. The pressures must balance according to Newton's 2nd law - otherwise it wouldn't stop compressing.

Do they mean that the water shoots out of the pipe at pressure of 50-100 PSI?

Yes.

How can one pressurize water (or any other liquid) ?

By trying to pump more water inside, thereby flexing the sides of the tank a tiny bit, making them press harder inwards. This harder pressing of the walls increases the pressure. Just like blowing air into a balloon until it expands; the balloon "wall" is flexing and expanding, but it presses back and tries to push the air out if it could.

If I put a membrane in a sealed tank that separate the water from the air, and then I compress the air to lets say 50 PSI, then it can be said that the water are pressurized to 50 PSI?

Yes. Again the answer is Newton's 2nd law: if nothing moves, all forces must balance. The water must press just as much on the membrane as the air does, since the membrane doesn't move.

can you remind me how to find their velocity? it comes from bernoulli?

Bernoulli is helpful, yes. Much is easily found on Google (otherwise this is for a new question).
A: They mean that if you were measuring the pressure on the walls of the tank (without opening up the tank or anything like that), it would read 50-100 PSI.
You can pressurize a liquid by applying force on it while it is constrained.  Since that force cannot go towards compression very well, it just pushes out in every direction, increasing the pressure.
Looking into hydrostatics should be able to give you a lot more information on the subject.
A: I think some commenters are reading too much into the question, the O.P. just wants to understand what is written about the tank. A quick google shows that domestic water pressure is up to about 80 psi. The tank is designed to contain water at a pressure range from 50 to 100 psi plus a factor of safety (usually 4 but water heaters are dangerous so it is probably higher).
The water pressure is supplied by standing head pressure from water towers or pumps. When water is not running in a pump designed for a single house they install a bladder tank like the membrane you mentioned. The pump compresses the air in the bladder tank and is switched on when a pressure drop is detected.
Your final question " ( and that means that if I open a valve in water side of the tank, they'll shoot out at 50 PSI ? can you remind me how to find their velocity? it comes from bernoulli?)" is confusing. Pressure is read with a gauge and there are many designs, velocity can be derived from pipe diameter, flow and pressure but I cant recall (without google) if Bernoulli is credited with that equation.
Drew K
