Conservation of energy problem with water hose? When we squeeze the end of the pipe while watering plants , the water speeds up , but the amount of water being released is the same ? From where does this excess kinetic energy come from ? 
 A: It is tempting to think that the reason the water speeds up is that the volume rate of flow remains constant as the area of the hose opening decreases.  However, this is not correct (just imagine what happens if you decrease the area to a pinhole--you will certainly not get as much water through).  It is not the volume rate of flow that remains the same, but the pressure at the source (I mean, you could set up a special constant-flow pump, but I'm assuming you're just using a municipal water source).  The thing that determines the speed with which the water exits the hose is the pressure just inside the end of the hose.  With a wide open hose, this pressure is small.  The water moves through all the plumbing and the hose just fast enough, with pressure dropping the whole way due to friction, that there is basically no pressure left where it leaves the hose.  If you squeeze the end of the hose, introducing a restriction, you decrease the volume rate of flow, and therefore the speed of the water through the plumbing.  The pressure drop along the way is less (less speed = less friction) so there is more pressure left at the end of the hose, and the water squirts out with higher velocity. 
The energy per unit time of the water leaving the hose is the volume rate of flow multiplied by the pressure at the exit.  It is highest for a partially constricted exit, when neither the pressure nor flow is near zero.  It may seem counterintuitive that you can increase the energy of the exiting water by blocking the flow, but such is the case.  In answer to the question of where the increase in kinetic energy of the water after it leaves the hose comes from, it is from potential energy which the water in the hose has by virtue of its pressure.  As the water leaves the hose, the pressure drops and the potential energy is converted to kinetic.
A: You probably have a pump.
Okay such a single line may feel tl;dr, but that would actually be the pinpoint answer, given that you said "the amount of water being released is the same" --- which I assume "in the same amount of time".  If the water flow reduced, the answer may have been a bit different.
A: It gets that "lost" kinetic energy from an engine or a water pump that is constantly "pushing" the water forward and not letting it stop and start going back when it gets to the small hole.
So the answer here is that the engine gives water the energy needed to go on, and how the engine gets that energy that is another story.
A: Because water is an incompressible fluid and when you squeeze the end of a pipe you are decreasing the cross section area so the velocity has to increase(check the continuity equation) and thus the KE too. 
A: Since mass=density×volume, m=dAx
Since the kinetic energy remains conserved 
K.E=1/2mv^2=1/2(DAx)v^2.
 As K.E is constant, as Area decreases velocity must increase.
A is area, v is velocity and x is length of water column. 
