This is going to be long:
Forgive me if this sounds pedantic, but whenever someone asks about fluid flow, I like to give a detailed description. I answer assuming that the inquirer knows very little about the subject just in case the person actually doesn’t.
For the portion directly relating to the hose, scroll down toward the bottom, but I encourage you to read the whole thing...
Water has weight, and as you increase the height to which you are bringing the water, the weight of the water pushes down on itself. One component of pressure (the reason why there is so much pressure on the ocean floor) follows the relationship:
P = (density)*(acceleration due to gravity)*( height).
Where height is the change in elevation from the surface of the water to whatever point at which you want to measure the pressure.
This is one part of the back pressure that all piping systems see. It is also why if you were to tap into a high pressure water main with a long vertical pipe, there is an elevation at which the water would simply stop rising because the weight of the water pushing down on the water main is creating a pressure which is equal and opposite to the water main pipe's internal pressure.
Hydraulic Head
The way piping works, is that as the fluid flows through a pipe from a pressure system to the open air (like your water main to the outlet of a faucet) it naturally flows in such a way that the pressure it experiences at the exit of the system is the same as the external pressure of the tank or system it is entering. In this case, the exit "tank" is your house, and the pressure of the atmosphere in your house (i.e. at the faucet nozzle) can be taken as the 0 psig. A water main has a positive pressure (let’s say for simplicity it is 50 psig) so somehow the water must “lose” this difference in pressure by the time it exits the faucet. As I alluded to earlier, one major way this difference in pressure is relieved is a change in elevation. If you were to install a faucet valve 40 feet above the water main and put a pressure gauge just below it, you would see that that gauge would read around 32.6 psig, as opposed to 50 psig, when the valve is closed. (40 feet increase in elevation = 40 ft head = ~17.4 psi drop for water).
Now let’s say that the faucet opening is a simple 90 degree bend 5 feet above the closed valve so that the total change in elevation from the water main to the faucet outlet is 45 feet. If you were to open the valve and then cover the faucet end, you would still see the 32.6 psig at the valve, and you would see that the faucet outlet has a pressure of around 30.5 psig due to the extra 5 ft of elevation at that point of measurement. The interesting stuff happens when you uncover the faucet. As I mentioned, the fluid must exit the faucet with the same pressure as the environment into which it is going. So somehow the water has to “get rid” of 30.5 psig.
The pressure differential causes the water to flow from high pressure to low pressure. Because water, like all fluids, is viscous, it experiences friction in the pipes which remove energy from the system. This reduction in energy reduces the effective head (pressure) of the system. The amount of energy lost is dependent on several components, but the main ones are the density and viscosity of the fluid, the roughness of the pipe, the velocity at which the fluid is moving through that pipe, and the total losses incurred depend on the total length of pipe that the water must flow through. The faster the fluid is moving through the pipe, and the more pipe there is, the more energy (and therefore pressure) is lost due to friction. We call this “head loss”. (read
Darcy-Weisbach Equation)
As with most things in nature, the system will seek equilibrium. Flow velocity is dependent on the pipe diameter and the flow volume (i.e. gallons per minute). Since the pipe diameter of your house doesn’t vary based on conditions, the thing that varies is the volumetric flow rate. When the valve is wide open, the system will push a large volume of water through your pipes. This large volumetric flow of water will be going at a very high speed and create a lot of friction head loss. Unsurprisingly, just enough water will flow through the system to create just enough friction to lose exactly the amount of pressure by the time it exits. So when the valve is open you get high volume and high velocity.
When you close the valve some, you get a
local increase in velocity due to the restriction in the opening in the piping; it will also have to change direction as there is an obstacle in the way. The water will flow very quickly around the valve, but will slow down as it enters the pipe just after it. The valve’s purpose is not to restrict velocity, nor to restrict flow, it is to generate head loss. When the valve is half closed, a lot of energy goes into forcing the same volume of water that was flowing before the valve through the smaller opening (conservation of mass). Piping engineers sometimes find it handy to look at valve losses as equivalent lengths of piping. For instance, in a 1” pipe, a gate valve at 50% open results in the same amount of the losses due to friction as you would see if the valve were simply replaced with approximately 25 feet of straight piping (not to be confused with 25 feet of elevation), at 25% open that might jump to the equivalent of the losses in 75 feet of piping. If you have 75 feet of piping, and then a 1" gate valve opened 25%, your system will lose the same amount of energy due to friction (head loss) as if there was twice as much piping!
What this means is that as the valve closes, the amount of energy lost at that point increases. These losses reduce the amount of head loss that would otherwise have to be lost due to flow velocity in the rest of the piping. Thus, less volumetric flow is required to be pushed through the system, which in turn results in a lower overall velocity elsewhere in the pipe.
So, when the valve is almost totally closed, what happens is that the water is forced through a tiny opening and does so at a
very high velocity
locally but because the losses incurred getting the flow through that opening, there is a relatively low volumetric flow rate required throughout the rest of the pipe to result in the necessary pressure loss. So while the velocity is very high at the valve, in the 1” pipe it is much lower.
First off, regarding the hose, you are not increasing the water pressure coming out. That water is exiting with a pressure of 1 atm but it is exiting with a higher velocity, it goes further because it's exit velocity is higher, not the pressure. What you are seeing when you cover the end of the hose is that
local increase in velocity due to the restricted flow area which you would also see if you took a
Fantastic Voyage trip into the pipe and viewed the flow just downstream of the valve. Creating that restriction acts like the valve by creating losses. What this does (though you might not be aware of it) is reduce the volumetric flow rate required to generate the losses to balance the system. So while the velocity at the hose exit may be higher than if your thumb wasn't there, the volumetric flow is actually lower. You can test this out. Get a bucket, a hose, and a stopwatch. See how long it takes to fill the bucket with the hose wide open, then press your thumb over the opening and time it again. It will take longer with your finger covering the hole!
So to sum up: The velocity
does increase locally at the valve when it gets progressively more closed due to the reduced flow area, but because the losses are greater as the valve closes, a lower volumetric flow rate is required to balance the pressures in the system, thus there is a lower overall velocity in the pipe.
