#### Jadnashua

##### Retired Defense Industry Engineer xxx

The water coming out of a shower head is very much determined by three basic principles:

- the incoming pressure

- the restriction in the head based on the number and size of the nozzles

- minimize friction by having a sufficiently sized supply line (i.e., not try to get the water to flow too fast which lowers pressure because of friction)

What people often mistake for pressure OUT of the head is not what they think. To increase pressure in the water supply, you have to do one of two things:

- pump it faster resulting in higher pressure

- raise the supply (gravity, like in a water tower) resulting in higher pressure

The force of the water out of a shower head, simplifying it, is a fairly simple equation where FORCE=1/2*MASS*VELOCITY-squared.

What you want coming out of a shower head is to speed up the water, as you cannot increase the force supply to that motion. So, for a simple example, let's take some numbers, and ignore the units, as we're trying to see how things change as we tweak the numbers a bit. Let's say the mass = 10 and the velocity is 5 (5-fps is the max the copper institute recommends for hot water velocity in copper piping).

So, just looking at the numbers of water flowing through an unrestricted pipe, we'd have 0.5*10*5^2=125

That 125 (unitless) number stays the same if you put a restriction into the pipe. But, take a typical shower head, it has a maximum flow rate of about half of the unrestricted value...we substitute 5 where 10 was before, and since the force is the same, solve for the velocity. This now becomes square-root of (FORCE/0.5*5) or square-root of 125/2.5=7.07. So the velocity went from 5 to 7.07, or a 40% increase in velocity. Now, it's a little more complex than that, but just to get a feel for it, this is a good approximation. A nozzle, or restriction in the flow of a fluid causes it to speed up, to try to pass the same amount force through the restriction. A shower head doesn't create energy, or pressure, but maintains it on both sides. What does happen because of the restriction, is that the fluid speeds up to keep both sides of the equation equal. If you take a rain-shower head, because it has so many possible outlets, effectively, the force gets distributed across those numerous outlets, so the velocity doesn't need to increase. Only when the size and number of outlets causes a restriction does the velocity increase, and the number and shape of them determines how it ultimately feels to the user. Now, it's a bit more complex, and there are some frictional losses, but for a basic understanding, hopefully, this helps. If you want a more detailed explanation, read up on the Bernoulli Principle https://en.wikipedia.org/wiki/Bernoulli's_principle#:~:text=Bernoulli's principle can be derived from the principle,energy, potential energy and internal energy remains constant.

- the incoming pressure

- the restriction in the head based on the number and size of the nozzles

- minimize friction by having a sufficiently sized supply line (i.e., not try to get the water to flow too fast which lowers pressure because of friction)

What people often mistake for pressure OUT of the head is not what they think. To increase pressure in the water supply, you have to do one of two things:

- pump it faster resulting in higher pressure

- raise the supply (gravity, like in a water tower) resulting in higher pressure

The force of the water out of a shower head, simplifying it, is a fairly simple equation where FORCE=1/2*MASS*VELOCITY-squared.

What you want coming out of a shower head is to speed up the water, as you cannot increase the force supply to that motion. So, for a simple example, let's take some numbers, and ignore the units, as we're trying to see how things change as we tweak the numbers a bit. Let's say the mass = 10 and the velocity is 5 (5-fps is the max the copper institute recommends for hot water velocity in copper piping).

So, just looking at the numbers of water flowing through an unrestricted pipe, we'd have 0.5*10*5^2=125

That 125 (unitless) number stays the same if you put a restriction into the pipe. But, take a typical shower head, it has a maximum flow rate of about half of the unrestricted value...we substitute 5 where 10 was before, and since the force is the same, solve for the velocity. This now becomes square-root of (FORCE/0.5*5) or square-root of 125/2.5=7.07. So the velocity went from 5 to 7.07, or a 40% increase in velocity. Now, it's a little more complex than that, but just to get a feel for it, this is a good approximation. A nozzle, or restriction in the flow of a fluid causes it to speed up, to try to pass the same amount force through the restriction. A shower head doesn't create energy, or pressure, but maintains it on both sides. What does happen because of the restriction, is that the fluid speeds up to keep both sides of the equation equal. If you take a rain-shower head, because it has so many possible outlets, effectively, the force gets distributed across those numerous outlets, so the velocity doesn't need to increase. Only when the size and number of outlets causes a restriction does the velocity increase, and the number and shape of them determines how it ultimately feels to the user. Now, it's a bit more complex, and there are some frictional losses, but for a basic understanding, hopefully, this helps. If you want a more detailed explanation, read up on the Bernoulli Principle https://en.wikipedia.org/wiki/Bernoulli's_principle#:~:text=Bernoulli's principle can be derived from the principle,energy, potential energy and internal energy remains constant.

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