Control flowrate or pressure? Faucet and garden hose conundrum

[push33n]

Hello, I am confused why when we turn on a faucet on small, the water doesn't accelerate out of the tap like you would expect from Bernoulli's equation where a reduced area means a high velocity. It seem's like the faucet only regulates flow rate but not the pressure. However, if you connect a garden hose to the faucet, turn it on and cover the hose partially with your finger, the water will exit with a high pressure squirting a huge distance. I would like to know why does the water behave differently in these two cases? How is Bernoulli's equation interpretted for both cases of a faucet and a garden hose? Thank you.

 

[Travis_King]

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.

 

[michio kakhead]

Hello, I am confused why when we turn on a faucet on small, the water doesn't accelerate out of the tap like you would expect from Bernoulli's equation where a reduced area means a high velocity. It seem's like the faucet only regulates flow rate but not the pressure. However, if you connect a garden hose to the faucet, turn it on and cover the hose partially with your finger, the water will exit with a high pressure squirting a huge distance. I would like to know why does the water behave differently in these two cases? How is Bernoulli's equation interpretted for both cases of a faucet and a garden hose? Thank you.

Resurrecting a thread from the dead... sorry!

While it's clear that Travis is obviously intelligent and gave a very informative response, I’m guessing that he’s either a plumber or someone who likes to copy/paste stuff from Wikipedia to get noticed. In either case, he dropped a ton of knowledge that would almost surely be very overwhelming to anyone asking this particular question (no offense intended). Furthermore, I do not believe that travis ever actually answered the question at hand.

First off, the thread starter mentioned faucets and hoses. Normally, hoses will be fed by a large 3/4” pipe that’s very close to the main water source of the house and has very few twists and turns. The large pipe diameter equates to high flow and the short and relatively straight piping path results in very low pressure loss. Most modern bathroom sinks, on the other hand, are fed by smaller 1/2” main lines that have to travel a significant distance, often vertically (even worse). Furthermore, they normally reduce down to 3/8” flexible hose just before the tap, which greatly reduces flow. Keep in mind that the cross-sectional area of a 3/8” ID pipe is four times smaller than that of a 3/4” pipe. For those reasons, opening a bathroom sink valve the same amount as a valve on a hose bib outside the house will result in a slower (read: less forceful) flow at the sink faucet than the hose bib.

Now that we have that out of the way, we need to start talking about the real answer that the thread starter is looking for. It doesn’t require any complex equations to determine the water pressure differential at various fixtures throughout (and outside) the house. Instead, it requires an understanding of the difference between a thumb and a mechanical water valve. A thumb is quite squishy, flexible, smooth, and oddly shaped. It was made by God and is used to assist in grabbing objects or catching a ride on the side of a highway. A valve, on the other hand, was designed by an Engineer and is a solid and rigid metal object with hard edges. It was machined to tight tolerances for the sole purpose of sealing/arresting water flow, and it usually does its job quite well.

For the sake of convenience, let’s imagine that the the hose is connected directly to an open pipe on the outside wall and the hose bib valve has been moved all the way out to the end of the hose. Yes, there would be a minor loss of pressure as a result of the added length of the hose, but that is a moot point. Instead, let’s imagine that the pressure at the end of the hose is now the the same as it was at the exterior wall. So, if the pressure at the hose bib on the wall outside the house was 50 psi, we are now seeing that same 50 psi at the relocated (and closed) bib valve at the end of the hose. If we were to open that valve just a tiny bit (let’s say 2%), water would slowly dribble out. We are now to the point where the original question can be discussed without other variables tainting the conversation.

The original poster asked why the water does not exit a barely-opened hose bib at an increased velocity, similar to what happens when a thumb is placed over the end of an open hose. After all, physics class taught us that water (and any incompressible substance) should travel faster as it’s forced into a smaller area. That is true, but only if there is sufficient pressure pushing on the water. If sufficient pressure does not exist, then the liquid will travel through the restrictive smaller opening at a slower rate of speed. If the pressure was to magically increase to 5000 psi (and all the piping and valves were reinforced to accommodate the increased pressure), water would immediately shoot out of that same 2% opening with deadly potential. It would be moving so fast and with such force that it could easily cut through skin and flesh and cause life threatening injuries.

Okay, back down to the real world with a pressure of 50 psi. If one was to open the same hose bib valve all the way and attempt to cover the opening with his thumb, he would not get anywhere close to the 98% restriction in flow that was possible using the valve. No human has a thumb strong enough to seal the end of a hose when the water is being motivated by 50 psi. Anyone who has ever attempted to stop a household water leak by plugging it with something quickly realizes that it is a futile attempt. The pressure required to seal the opening of a 3/4” ID pipe @ 50 psi is almost 30 lbs. Additionally, the seal must be close to perfect to have any real effect. My guess, in this example, is that a thumb could only provide a maximum flow restriction of around 20%, if that, which is not enough to significantly restrict the water flow.

In addition to the thumb being too weak to sufficiently restrict flow at 50 psi, it doesn’t seal well, either. Skin, flesh, and fat are squishy and flexible, which means that the water never encounters any substantial resistance or change of direction. On the contrary, your thumb acts more as a means to redirect and focus the stream of water than to restrict it. Skin is also quite smooth, which means that friction/turbulence is minimized, further increasing the effectiveness of the mighty thumb. This is why the end result is a smaller, more focused stream of water that is traveling faster and more forcefully than one which flows from a slightly opened hose bib valve.

To push33n: if you are still alive and reading this forum, hopefully my response helped you understand things a bit better... that is, if someone else has not explained itnto you in the past fifteen months. :)

 

[Travis_King]

While it's clear that Travis is obviously intelligent and gave a very informative response, I’m guessing that he’s either a plumber or someone who likes to copy/paste stuff from Wikipedia to get noticed. In either case, he dropped a ton of knowledge that would almost surely be very overwhelming to anyone asking this particular question (no offense intended). Furthermore, I do not believe that travis ever actually answered the question at hand.

For the OP and any other interested readers (as this is a common question) I am a mechanical engineer working in the mining and minerals processing industry. I deal with this stuff almost literally every day.

It is an old thread so I was hesitant to reply after reading your response, but I'm not sure you understand the principles in question here either, so I want to dispel some of the inaccuracies in your response.

If we were to open that valve just a tiny bit (let’s say 2%), water would slowly dribble out. We are now to the point where the original question can be discussed without other variables tainting the conversation.

You've only confused things by this point. The OP wanted to know why water doesn't shoot out of a faucet at high velocity when the valve is mostly closed (let's use your 2%). It's a valid question from someone who just became familiar with Bernoulli's equations. One sees a volume of water flowing at some rate, then forced through a small opening; I can understand why one would think it would speed up. I address this toward the end here.

It requires a better understanding of how liquids function in piping systems to understand why water doesn't shoot out of a faucet. At the very least, one should understand the principles I laid out in the last paragraph or two of my previous post.

The original poster asked why the water does not exit a barely-opened hose bib at an increased velocity, similar to what happens when a thumb is placed over the end of an open hose. ... If sufficient pressure does not exist, then the liquid will travel through the restrictive smaller opening at a slower rate of speed.

This is sort of correct, but I don't think for the right reasons...

Additionally, the seal must be close to perfect to have any real effect.

This simply isn't true. Any restriction will have a real effect. If your thumb is covering the hose end enough that your are able to ask whether it is perfect or not, rest assured you've affected the flow pretty significantly.

My guess, in this example, is that a thumb could only provide a maximum flow restriction of around 20%, if that, which is not enough to significantly restrict the water flow. In addition to the thumb being too weak to sufficiently restrict flow at 50 psi, it doesn’t seal well, either. Skin, flesh, and fat are squishy and flexible, which means that the water never encounters any substantial resistance or change of direction.

A thumb can certainly restrict the flow greater than 20%, much, much more than that I would think. Either way, a 20% restriction in the flow path will certainly alter the flow rate. Industries which use water in their processes use this principle every single day with control valves.

While I agree that most people probably can't fully stop a hose with their thumb this isn't because the thumb is squishy, it's because it requires, as you said, a lot of force to keep it there and we aren't generally strong enough.

Squishy things can create great seals with enough applied pressure, that's why people use gaskets. Though in this case, you are right that the thumb mechanism is not adequate for a complete seal.

On the contrary, your thumb acts more as a means to redirect and focus the stream of water than to restrict it.

Redirection of flow requires energy, that energy is then lost by the water. Flow redirection has the same basic effect on water as a flow restriction, they both cost energy.

This is why the end result is a smaller, more focused stream of water that is traveling faster and more forcefully than one which flows from a slightly opened hose bib valve.

Well, it's going faster anyway. What happens is this (hopefully I can explain it clearly, it's somewhat tough to visualize):

Say you have an house main that has a pressure of 50 psi at the closed hose bib. Then you've got some length of hose after the bib. You open the bib fully and water, being claustrophobic , leaves the main seeking to shed itself of the uncomfortable pressure. As I mentioned in my other post, enough water will flow through the pipe so that that 50 psi is ablated (due to friction losses, and energy losses due to bends or obstructions, like partially closed valves) to atmospheric pressure when the water exits the hose.

It's interesting what happens when you cover part of hose end with your thumb. By doing this you both create a restriction in the flow area, and you redirect the flow of the water. Both of these things create appreciable pressure loss. Because energy (and hence pressure) is lost to these restrictions, a smaller volume of water is required to flow through the pipe in order to ablate the pressure/stored energy via friction; less water flows through the pipe. But, though the volume of water is smaller, the velocity of the water is higher because, as you learned in physics, and as Bernoulli told us, a volume of incompressible fluid will flow faster through a reduced area.

Perform the bucket and stopwatch test, it's a pretty neat experiment.

The one thing I agree with you on is that the valve is a much better at restricting flow. Water dribbles from a partially opened bib because the opening the water must pass through is so small that the water loses a ton of energy trying to get through. It requires only a little bit of water to flow through the opening to reach equilibrium. If you were to match, with your thumb, the flow restriction created by the valve, you would see the same results.

Remember, water does not leave a hose at a pressure above atmospheric. A pressure washer doesn't shoot out water at high pressure. It uses the principle that if you highly pressurize water, then force it through a tiny opening, you'll get water with extremely high velocity. It's the velocity of the water which does the cleaning.

 

[HDoh]

But why does the water from my garden hose taste better than the water from my house faucets?

 

[HDoh]

But why does the water from my garden hose taste better than the water from my house faucets?

 

[russ_watters]

Necropost...locked.