DHyslop;93301 said:
This is kind of what I mean with the forest and the trees thing. Those factors are the same whether there's a vent or not so they cancel out--by even bringing them up you're pulling out the hand lens and looking at the tree bark. At best a distraction.
As opposed to hovercrafts and helicopters, which are directly relevant
I'll be pedantic--apology in advance:
hey, I like pedantry... so much I'll be pedantic back. But anyway, when 2 people smart enough to be able to understand something are at odds, it seems like pendantry and experiment are all that's left. Er, unless we prefer a "hearts and minds" campaign to getting to the actual answer...
1. The pump has a maximum efficiency where as much of its energy as possible is being used to move water. There's an ultimate maximum efficiency if it was moving water horizontally without friction. That's not meaningful to our discussion at all, we care about a relative max efficiency which is the maximum efficiency it can have at the identical given conditions of both our scenarios ("the fight to rise to the upper tank and resistance in the pipe..."). I assumed this was tacit to the discussion so I believed the term "maximum" unmodified would be adequate.
The reason I'm not too keen on the name "maximum" it's the maximum given a bunch of stuff, and we seem to disagree on whether messing that stuff will make a difference in the efficiency of the pump. But I'm ok with thinking of it as the same efficiency it has in the closed system with no vent at all (or with the valve closed, which I think we agree is the same thing, right?) A more direct reason I care, though, is that your pinhole is changing the flow resistance to something that'll effect the pump's efficiency.
2. As you pointed out, the pump has a minimum efficiency of zero where none of its energy is being used to move water. All of the energy is being spent to hold that water. We know that the energy is holding the water because if we cut off the supply of energy the water is no longer held. A plug is in no way an analogy because a plug does not hold the water only if it is consuming energy.
In my worldview, this description has a subtle problem in it. When the pump is at zero efficiency, it is pumping against a pressure that is causing it to be unable to move any water. Therefore, all of the energy going into the pump is being turned into something other than flow (which moves water, and does mechanical work). Ultimately, this is heat, although it may stir up the sump or something. The pump really doesn't see anything beyond the pressure it's fighting against at its outlet, so it isn't doing anything different when that pressure is caused by a column of water than it is when it's caused by a cork. Although the cork has to be able to hold back the same pressure as that column of water, which is what I was getting at in the other post; the cork or outlet pipe or something will deform, and store some mechanical potential energy to respond passively to the pressure the pump generates until the pressure either overwhelms the pump down to zero efficiency, or overwhelms the cork. Or melts the windings in the pump motor or blows a gasket or whatever.
3. The pump has that minimum efficiency (one extreme end) when it is holding water at its maximum hydraulic head. All the energy is spent supporting the water, none is spent moving water.
Nope, all the energy is spent pushing on some pressure that's pushing back, which leads to a lot of heat generation but no mechanical work. The fact that the pressure is caused by there being a column of water there is immaterial; it could be a piston and a big rock, it could be a big spring, it could be shock absorber from a 74 trans am, it just has to be something that, when pushed, wants to push back. And if the pusher can push back hard enough without failing, the pump is turned into a heater, pretty much.
However, it is true that without the pump churning away, something other than the pump would have to hold back that force. But that could be a passive thing like a shut valve. In fact, if there were a valve right at the pump outlet, shutting the valve wouldn't change the pump's view of things anyway, because it's maintaining the max pressure it can with no flow, and it wouldn't change the column of water/spring/whatever side, because all it knows is that it's pushing with pressure Pmax on something that isn't yielding.
I know this seems extra bonus pedantic, but I think you're confusing "turning energy into heat with the side effect of maintaining pressure" with "spending energy on the mechanical work process of moving water." It's certainly valid to say that the pump running at zero efficiency is causal to the pressure being maintained, but when talking about conservation of energy, or mechanical work, or conservation of momentum, the pump is doing zero work, nothing has any net momentum, the pump's energy draw is being converted into heat, and past the pressure being Pmax at the pump outlet, the rest of the system is just sitting there.
We're just looking at steady states--any transition periods between these end-members (say the first few seconds after opening a hole) are ephemeral and their discussion offers no clarity.
sounds good to me
4. We now have two end-member scenarios: in one, all the pump's energy is holding up water. The other, all the pump's energy is moving water. Lets put this together in a continuum of infinitessimal steady state conditions between the two:
repeat complaint that the pumps energy is applying force to counter a pressure, which is only indirectly holding up water. The actual energy is going to heat, no energy is going into the changing the pressure.
a. All the energy is holding water up, none to flow. The water level in the vent is at max pump head.
As weird as it seems, none of the energy is actually going into holding the water up. The pump is in an equilibrium where, because of the opposing force/pressure, the pump can't put any more energy into the column of water, but the column of water pushing back can't put any of its potential energy back into the pump, it's a Mexican standoff. (you may have gotten the point for being first to mention hovercraft, but I clearly score for being the first to invoke an image from a spaghetti western!)
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