Water pressure through narrowing funnel

[gloo]

In the picture i have included I was wondering if the same downward force (black arrows) applied in the diagrams would result in an increased pressure as the water comes up through the same size hole.

I am assuming that both Diagram B and C will result in a higher pressure because of the narrow or funnel shape because more water is forced at a time through the hole with the same given force? If not can someone explain why?

 

[russ_watters]

The funnel shape creates a more efficient flow pattern, that's all. For the orifice, some of the water tries to make a 90 degree turn to get out and that results in an energy loss. So for each of these cases, you start with Bernoulli's equation to calculate the velocity through the orifice and then you multiply by the flow coefficient. Typically an orifice plate coefficient is around 50% while a nozzle is around 75% (if I remember correctly...you can google them).

 

[gloo]

So is it erroneous the way this toy company states that their water cannon toy...which is just a funneled cone with handles, uses the "Venturi effect" which when you force water up a narrowing cone, causes greater water pressure, and thus the water can squirt 30 feet? Isn't it pressure that makes the water squirt further??

Here is the link.

http://www.geyserguys.com/science.php

 

[russ_watters]

It is an oversimplification but not really wrong: both the orifice and nozzle use the venturi effect, the nozzle just does it more efficiently.

[Edit: actually the article makes no mention of a comparison to an orifice, so it isn't wrong at all.]

 

[CWatters]

My bold...

http://www.geyserguys.com/science.php

The pulling force by the user is converted to a water jet by the VENTURI EFFECT, which states that as the water travels through the decreasing diameter of the GEYSER GUSHER cone, the pressure increases,

http://en.wikipedia.org/wiki/Venturi_effect

The Venturi effect is a jet effect; as with a funnel the velocity of the fluid increases as the cross sectional area decreases, with the static pressure correspondingly decreasing. According to the laws governing fluid dynamics, a fluid's velocity must increase as it passes through a constriction to satisfy the principle of continuity, while its pressure must decrease to satisfy the principle of conservation of mechanical energy.

 

[russ_watters]

Oops, missed that. Still the Venturi effect, but they did state how it applies incorrectly.

 

[gloo]

so what is the explanation of the water traveling so far (30feet) with a simple pull? The water pressure decreases as it is in the narrowing funnel, but comes out from the nozzle at higher pressure no?

 

[russ_watters]

No, the water exits the nozzle with zero pressure because it is open to the atmosphere. The job of the nozzle is to convert the static pressure inside the tube into velocity pressure of moving water, while losing as little of that pressure as possible due to inefficiency. Then based on the exit velocity, you can calculate distance using projectile motion calculations (and the assumption that the stream remains coherent).

 

[gloo]

Russ...just a couple of more questions:

1. you said "converts static pressure inside the tube" -- That is the pressure created by the person pulling on the cone. What is the parameter that will contribute to the magnitude of the static pressure?

a. size of force (obviously)
b. length of cone?
c size of hole?

I guess the force is obvious, but how about size of the hole and the length of the cone? I assume the size of the whole for sure..not the length of the cone.

2. You said "velocity pressure of moving water"?? So this is high velocity, lower pressure water?

 

[Sungamr]

The static pressure of the fluid is a function of the force / cylinders area as a function of its diameter. (I conveniently forget about the exit hole and friction losses, they should be negligible for calculating the static pressure).

To make the math simple let's imagine a square tube with 1" side walls. A section of the tube will then be 1x1 = 1 square inch. Let's say that the user apply a force of 10 pounds. Then the pressure will be 10/1 = 10 pounds per square inch. It's as simple as that.

The shape of the piston (cone) does not matter. One way of looking at it is that (taking our square tube as an example) if you compress the gun 1 inch, one cubic inch of water will be ejected, as every point of the piston have moved exactly one inch relative to where it started regardless of the shape.

A deciding factor for the ejection speed (aside from the nozzle design as pointed out by @russ_watters) is consequently the diameter of the cylinder. If we make it half the area we will get double the pressure but only half the volume. Physics forces us to make a compromise between range and soakiness.

Edit: Technically you should subtract the area of the nozzle hole when calculating the pressure, but in this design it should make very little difference. Friction, mainly from the sealing between the moving parts should of course be factored in for the truly detail oriented.

 

[gloo]

Thanks for your input Sungamr - I really appreciate the help I am getting. So going back to discussing the ejection speed issue. I have some questions:

1. The ejection speed is increased, and thus can travel further correct?
2. The trade off for increased speed, is less pressure for this water stream?
3. Thus if the force in diagram B and C is applied, the water will squirt higher (travel further) as a consequence of increased velocity?
4. The shape of the cone and the smaller the opening, will result in a larger exit velocity and further distance?

 

[gloo]

Russ, Sungamr? Please if you can help with my questions? Anybody? Especially question # 4. I don't know where else to go and I have talked to my other friends who were decent in Physics in high school...but they were not sure. They even mixed up the higher pressure argument cause of the cone shape (i.e. smaller area = greater pressure).

Anybody??

 

[CWatters]

I believe 4 is basically correct because the faster you launch something the further it goes (google projectile motion).

However there will probably be a limit at which point making the hole smaller does not increase the distance achieved. Sadly I'm not an expert on fluid dynamics but I suspect that the diameter of the jet has an effect on it's stability - eg it might break up into droplets sooner if too small ?

I guess you also need to consider the power source - the human pulling on the cone. Humans can only generate a limited amount of mechanical power so that would also put some sort of limit on the amount and velocity of the water jet.

 

[gloo]

Thanks for responding CWatters :)

@ Russ Watters - Please if you can just help with my inquiries, as I value your help and do not know where else to get answers:

The water exits at a higher velocity. Russ Watters mentions the term "velocity pressure" -- This means that the squirting stream of water can push further or higher up, but the overall energy is conserved. The flow will be faster and higher, but the overall flow out of the nozzle will be the same versus say an orifice.

So thus besides the net force down and the diameter of the entire piston, we can use employ 2 factors to get the water to come out at a higher "velocity pressure" by adding:

1. longer and wider funnel that makes the flow more efficient.
2. making the nozzle smaller.

Optimizing these 2 factors, we can make the water push out faster and higher.

 

[russ_watters]

Sorry for the late replies:

1. you said "converts static pressure inside the tube" -- That is the pressure created by the person pulling on the cone. What is the parameter that will contribute to the magnitude of the static pressure?

a. size of force (obviously)
b. length of cone?
c size of hole?

I guess the force is obvious, but how about size of the hole and the length of the cone? I assume the size of the whole for sure..not the length of the cone.

The force is what you supply with your arm. The area is the total cross sectional area of the piston, not the area of the cone or hole.

2. You said "velocity pressure of moving water"?? So this is high velocity, lower pressure water?

Any fluid has a static pressure and any moving fluid has a velocity pressure as well. They are two different things, but related by Bernoulli's Principle:
http://en.wikipedia.org/wiki/Bernoulli's_principle

1. The ejection speed is increased, and thus can travel further correct?

Yes: that's a projectile motion problem.

2. The trade off for increased speed, is less pressure for this water stream?

Again, there are two different kinds of pressure: velocity pressure and static pressure. Static pressure is zero in the atmosphere.

3. Thus if the force in diagram B and C is applied, the water will squirt higher (travel further) as a consequence of increased velocity?

Higher than what?

4. The shape of the cone and the smaller the opening, will result in a larger exit velocity and further distance?

Shape of the cone yes, smaller opening no. As I said above, the pressure is a function of the total area of the cylinder, not the area of the orifice. The caveat being that it may become harder to apply the force if the piston moves quickly. But below a certain size hole, there isn't much of a difference.

However another caveat is that the stream of water will stay more coherent if it is thicker.

 

[gloo]

1. Russ Watters said: "higher than what?"

I guess higher than Diagram A with no cone against the orifice

2. Russ Watters said: "Shape of the cone yes, smaller opening no."

a. So the shape of the cone, in what sense?
b. I am assuming there is an optimal shape?

In the end, does this higher velocity stream of water, have a higher penetration ability then? Can it say break a membrane of certain strength better because of the higher velocity when it hits the membrane (everything else the same?)

Thanks for coming back to help Russ. I so appreciate your help.

 

[russ_watters]

1. Russ Watters said: "higher than what?"

I guess higher than Diagram A with no cone against the orifice

Yes, the cone should make the acceleration of the water (conversion of static to velocity pressure) more efficient.

2. Russ Watters said: "Shape of the cone yes, smaller opening no."

a. So the shape of the cone, in what sense?
b. I am assuming there is an optimal shape?

Well, the cone should probably be curved, not straight, to make the acceleration smoother and eliminate the sharp edges. Beyond that, it gets difficult to predict in general.

In the end, does this higher velocity stream of water, have a higher penetration ability then? Can it say break a membrane of certain strength better because of the higher velocity when it hits the membrane (everything else the same?)

I suppose it depends on the membrane, but probably, yes.

 

[gloo]

Russ, so I guess it's fair to say, that the size of the cone does matter? For instance, diagram B has smaller cone and less water is forced into the tapered opening. But in diagram C, a larger volume of water is forced or channeled more efficiently towards the nozzle?

Also, is it correct to say that the volume of water that comes out of the tapered cone has a higher force versus the one with just the orifice? I am assuming this because I guess higher velocity, whereas velocity is proportionate to energy? (E=0.5*m*v*v)

Thank you so much Russ.

G

 

[gloo]

Hey Russ, hoping you can answer my two questions above? Especially the second question (before I spend money to try something).

g