Novice Electrical Guy with a Mechanical Question

[FordTruckMan]

Hello All.
This is my first post, and I hope it is not too simplistic, but I am out of my normal line of work here.

I am trying to understand the relationships between flow, velocity, and cross sectional area with gases and fluids(air and water). Imagine a large vertical, cylindrical tank filled with water. It has two pipes coming out the side, at the same elevation, and they are the same length(24") with a ball valve to open and close water to them. They terminate in free air. One pipe is 1" diameter, the other is 6" diameter. If I open both ball valves, water will come out both pipes and spill onto the floor. My question is this: Will the velocity, flow or pressure of the water be significantly different between the two pipes?(if all measurements are taken halfway from the tank to the end of the pipe) My feeling is that the larger pipe will have greater flow, lower velocity, and increased pressure, vs the smaller pipe. Is this accurate? What about the same scenario, but with the tank being filled with air instead of water, and being kept at a constant pressure of say 50 psig? Would the air react any differently than water? I realize air is just a less dense "fluid", right? I feel it would behave the same.

My second scenario, is with air supplied through a heating duct. Imagine a constant pressure of say 15"H2Og on one side of a piece of sheet-metal duct. This duct has 2 holes in it. One is 1" diameter, the other is 3" diameter. Will the flow, or velocity of air be any different between the two holes?(If measured with a meter held 1" from hole on exit side) I feel the velocity would be slightly greater measure at the smaller hole, but flow would be the same? Is this correct?

I apologize, as I'm sure this is basic stuff, but I am not a mechanical guy.

Thanks to all who reply!

 

[anorlunda]

Those questions sound ideal for a bit of home science experimentation. Why don't you try it . Then post here what you observed.

 

[FordTruckMan]

While I can appreciate that notion, I was hoping for some input on my questions...

 

[Drakkith]

My question is this: Will the velocity, flow or pressure of the water be significantly different between the two pipes?

Absolutely.

My feeling is that the larger pipe will have greater flow, lower velocity, and increased pressure, vs the smaller pipe.

The larger pipe will have a greater flow rate, but a lower velocity and lower pressure. The small pipe flows faster precisely because the pressure is higher.

 

[gmax137]

...The larger pipe will have a greater flow rate, but a lower velocity and lower pressure...

Isn't the pressure drop across both pipes equal? Tank pressure at the pipe's elevation minus atmosphere?

If there were no friction/form losses the velocities would be equal too, just converting the elevation head at the tank nozzles to velocity. Then the ratio of the flow rates would just be proportional to the ratio of the areas.

For real pipe with real losses, there are differences due to the pipe size, but the differences are pretty small.

 

[Drakkith]

Isn't the pressure drop across both pipes equal? Tank pressure at the pipe's elevation minus atmosphere?

Not sure. I was thinking that the total pressure on both pipes was the same, but the pressure per area was higher on water in the smaller pipe, which is why it flows faster.

 

[FordTruckMan]

Thank you for the responses so far. Now you see my confusion. I have changed my mind about what the answers were many times, but i still am not sure.

 

[Q_Goest]

I am trying to understand the relationships between flow, velocity, and cross sectional area with gases and fluids(air and water). Imagine a large vertical, cylindrical tank filled with water. It has two pipes coming out the side, at the same elevation, and they are the same length(24") with a ball valve to open and close water to them. They terminate in free air. One pipe is 1" diameter, the other is 6" diameter. If I open both ball valves, water will come out both pipes and spill onto the floor. My question is this: Will the velocity, flow or pressure of the water be significantly different between the two pipes?(if all measurements are taken halfway from the tank to the end of the pipe) My feeling is that the larger pipe will have greater flow, lower velocity, and increased pressure, vs the smaller pipe. Is this accurate?

I guess you're trying to understand this intuitively. You can calculate it of course. For pipe flow, you would typically use the Darcy Weisbach equation. I did that and found the velocity of the water in the 6" pipe was significantly higher than the 1" pipe for some arbitrary verticle length of pipe. After thinking about it, it occurred to me you could consider this intuitively by using a thought experiment that looks at two extremes. Rather than a 1" pipe and a 6" pipe, consider a very small pipe, say much smaller than 1" and a very large pipe, much larger than 6". For the large pipe, consider a pipe who's diameter is many times larger than the length/verticle distance the pipe goes through. You might imagine for an exceedingly large diameter pipe like this, the wall friction has no siginficant affect on the water, and the water simply drops through at a rate dictated by the acceleration due to gravity. So that's the fastest velocity the water could attain through a verticle pipe. For a very small pipe, frictional losses between the water and pipe walls slow it down, so the velocity of the water is going to be significantly lower than the velocity determined by the acceleration due to gravity. If this intuition is correct and assuming there's no other factors that affect velocity, it says that as the pipe diameter increases, frictional losses with the wall go to zero so velocity should increase for the larger diameter pipe.

Unfortunately, it's not that simple. There's a transition zone (also called "critical zone") that's a function of Reynolds number (which is a function of fluid velocity). As Reynolds number increases, the friction factor decreases in the laminar zone (up to Re ~ 2000). From 2000 < Re < 4000 (aprox values) there's a transition zone where flow could be turbulent or laminar or a mix I suppose. Above Re ~ 4000, you get turbulent flow. For Re = 4000, the friction factor has increased from the point it was at Re = 2000 meaning that the flow is more restricted so you might expect velocity to decrease. I played with a calculator for a while and tried to find one pipe with an Re = 2000 and a slightly larger one with Re = 4000 and found the velocity in the larger pipe was still higher than the smaller pipe, but that isn't to say it will always be. It's still a bit more complicated and you may want to consider sloped pipes to see how that affects flow. But suffice it to say, around this transition zone, you may find the larger pipe could have a slightly lower velocity than the smaller one. I just haven't been able to come up with a set of values that would prove this as there are a large number of variables that go into it.

 

[Drakkith]

Well, this is beyond my knowledge so I'm going to step out.

 

[Wes Tausend]

Thank you for the responses so far. Now you see my confusion. I have changed my mind about what the answers were many times, but i still am not sure.

FordTruckMan,

I'm glad to see some potential hotrodders on here. Our future automotive engineers can learn a lot here, especially the math involved in physics.

The two size holes in your proposed water tank will have equal pressure, and therefore velocity, because they are at equal height. If they were the same (or different) diameter at different heights, they would have different pressures and different velocities purely because of the height. There is simply more pressure near the bottom of the tank, just as there is more pressure near the bottom of a deep sea. In other words, the water in your scenario will pour out in equally curved streams and land on the floor in equal distances from the tank center in a P'ing-like contest. But the larger pipe will definitely produce more overall water flow.

You can compare this principle to electricity. Imagine you have two resistors connected to the same electrical potential and they both connect to ground at the other end. (Pressure corresponds to voltage, water flow to ampere current and pipe restriction size to resistor.) A voltage measurement across either flowing resistor will show the same voltage drop, in this case full applied voltage... or full pressure drop in the case of a tube exiting a water tank. The less restrictive pipe, or resistor will flow more current... or water. If you cap the pipes and measure non-flowing pressure at their outlet, they will measure exactly the pressure as per water manometer, at that height, as will that particular water height inside the tank. This is also true if one measures voltage to ground at the end of the disconnected resistors when in an open (non-flowing) circuit. Now keep in mind, as the water tank depletes, the equal pressures will gradually drop from both pipes to a dribble. Or in the case of a battery going dead, the voltage will gradually drop to zilch.

For your second scenario, filling the tank with air and keeping it at 50#, that is different. Now the pressure is ideally regarded as being the same everywhere in the tank, no matter the port height. In reality, there is a tiny pressure difference between the top and bottom because air, which is a fluid, does weigh some, just not as much as water. That is why I said ideally there is no practical difference.

Since the pressure is basically the same between the two pipes again, both velocities will be largely the same too. In other words a small fan held in either air stream will turn the same rpm, although two little fans might fit side-by-side in the large stream. Or better yet, a pitot tube for measuring air speed will read the same air speed for either opening.The overall volume will be very different again though, because the big pipe will certainly leak more volume of air. This scenario also holds true for your heating duct, where internal pressure is the same for both differently sized outlets. Different flow rates, but same velocity.

If you were to design an intake for an internal combustion piston engine, things would be different. Many of the same pressure rules apply to the average, but the length of a tube also responds to productive tuning when the air is pulsing from pistons. Water, since it is not very springy, does not respond to similar tuning. To study this effect, you might want to google "tuned pipe".

One other automotive engine effect is that since the rpm of the engine varies the amount of air ingested, the smaller intake tract typically reaches higher velocities at slower speeds (city driving) and the mass (like weight) of this slender moving column of air has more momentum once it is going. With careful planning, this sometimes helps fill the cylinder better at slower speeds which develops more efficient "lower end" torque.

Wes
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