A hydraulic pump, like all other pumps, moves water from a low point, A, to a higher point, B. But, unlike other pumps, a hydraulic pump has the advantage of requiring no external energy source to perform the pumping action. This might sound like it's completely against all the known laws of physics, but it's not--the water is put to work to pump itself.
Understanding how a hydraulic pump works can be bit of a daunting task because it deals with a medium--water--that, while we are familiar with it, we are not accustomed to thinking about it as an object that has inertia.
Inertia is a property that all objects have. It describes how difficult it is to get an object moving or to make it stop. The greater the mass of an object, the greater its inertia. Consider a golf ball on a hard surface. If you press your finger against the golf ball, it moves with little resistance. Once moving, it is also equally easy to stop. The golf ball has low inertia.
Now consider a cannon ball. If you were to give it a push with your finger, you'd find that it resists the force and wants to stay put. If you push harder, your finger will turn purple and bend in a strange angle, but eventually the cannon ball will begin to move. If you were to try to stop the ball once it's in motion, you'd notice that it moves your entire hand before coming to rest. This is because the cannon ball has a high inertia and resists being stopped.
If an object of high inertia can move your hand, there is no reason why it can't move something else, like water. Of course, there's the problem of getting the water in motion in the first place.
Actually it's not that much of a problem at all. Water on earth has the tendency to acknowledge the presence of gravity and flow to the lowest point. Everyone who has tipped over a glass of water knows this too well.
Once the gravity overcomes the inertial resistance of water and gets it moving, it will resist being stopped. Water wheels on old style mills are a good example of this. The flowing water of the river moves the giant wheel because its inertia is greater than the inertia of the wheel.
An inertial object, when accelerated by a force such as gravity, possess momentum. Inertia is neat, but momentum packs a punch. It is the product of the mass of the object and its current velocity, which is continuously increasing due to its acceleration. This explains why a high speed bullet can stop a man, but catching a thrown football has little effect. Roll that cannon ball down a steep incline and your arm will fall of if you try to stop it.
Suppose that cannon ball is not just one, but a line of them inside of a tube on a slight incline. Imagine that there is some sort of stop on the tube that prevents the cannon balls from coming out. Now, remove that stop. They would start to move down the incline slowly at first, but would quickly build up speed and have quite a force behind them. Snap the stop back on. What happens? The whole tube full of cannon balls gives a mighty jerk because it all of the momentum in the cannon balls has to be suddenly absorbed.
Imagine water is in that tube instead of cannon balls. Opening the stop and suddenly closing it produces exactly the same powerful kick as it did with the cannon balls. But there is one difference: the sides of the tube are elastic, albeit on a miniature scale, and expand a tiny amount to accomodate slightly more water. In the case of the cannon balls, the sides weren't able to compress because when the balls hit the stop, they weren't able to flow and fill up space like water is able to.
As a result of the force from the sides of the tube, the water is under a lot of pressure and would love to go somewhere. If you were to make a hole in that tube, you'd find that you had a miniature fountain squirting out of it. Squirting upwards, and in the right circumstances, above the water's source.
This is the basic first half of a hydraulic pump's operation. Water is accelerated down a tube that has an open end. It builds up speed thereby momentum. When a maximum speed is detected by a check valve (a valve that opens when a predetermined flow rate occurs), the valve snaps shut and pressure in the tube suddenly increases because all of the water that is coming down the tube at full speed has to stop. When a maximum pressure has been detected, another valve snaps open and the water shoots through it. This cycle then repeats.
But that's only the first half of the operation. While it is certainly able to move water up, there is a further step that improves the height that the water can travel and removes the pulsating action.
The burst of high pressure water is fed into the bottom of a tank. The tank is half full of water and half full of air. There is also a small outlet located beneath the water level. When the burst is let in, it compresses the air (the compression of water is negligible) and the valve snaps shut, leaving what is essentially an aerosol can of water. Whatever happens to be at the end of the outlet acts as the nozzle on the aerosol can, though often there is nothing at the end.
Shown here is a drawing of how a hydraulic pump works:
A hydraulic pump in operation.