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I live on the first floor of a seven story apartment building. We are considering our hot water options and one of them is a solar-powered water heater in which water is heated in a specialised device similar to an air conditioning condenser under the sun (very common in Israel).

Ignoring the fact that the device will need electric heating in winter, the heat loss through the pipe on the way down, and the wasted water while we wait for the hot water to make it's way to the faucet (all real concerns), I would like to disprove the imaginary concern of pressure loss after the round trip. My argument is that the pressure lost on the way up will be exactly compensated by the pressure gain on the way down, excluding losses due to friction in the pipe.

That leaves the question of how much friction is in the pipe. Googling the question I have found all means of formulae, diagrams, equations, etc, most consisting of variables that I don't have (such as the Hazen-Williams coefficient of all the pipe and fittings, the initial pressure and the flow rate). The truth is, I really don't need such an accurate assessment but rather just to know if the pressure drop would be "not noticeable", "noticeable but not a problem", or possibly "you can no longer do laundry". So for seven floors up and back down, through a flexible plastic pipe with an outside diameter of 16 mm (I don't know what the inside diameter is) and a few fittings, how can I estimate the percentage of pressure drop in layman's terms, not engineering terms?

In other words, I'm not looking for someone to do the calculus for me and give me a number, but rather I would like some help in deciding how to go about figuring out a rough estimate.

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Did you really mean 1.6 millimeters? You wouldn't get much of a flow rate through that pipe! –  John Rennie Jul 9 '12 at 9:30
    
Can you describe more precisely what the concern is? Am I right in thinking that the device is on the roof, and so people are worried that there might be a loss of pressure after the water has travelled up to the roof and then back down to the lower floors? Or is it something else? –  Nathaniel Jul 9 '12 at 10:26
    
@John: Thanks, I meant either 16mm or 1.6cm. I think that NASA once made a similar mistake in the vicinity of Mars! –  dotancohen Jul 9 '12 at 11:56
    
@Nathaniel: Yes, that is exactly the concern. We have had solar heaters on the roof in previous apartments, but never 7 stories up! I've actually already discredited the idea due to the waste of water while waiting for the hot water to get to the faucet, but I would like to either dispel or confirm the suspicion that their would be a pressure loss. –  dotancohen Jul 9 '12 at 11:57
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My gut feeling is that the pressure loss will be noticable, but managable with a small heating pump. 16mm diameter, however, seems awfully thin to me.

You need to consider several things: How much thermal power will your heating system deliver, and at what temperatures? From this you get the neccesary flow: $Q=\frac{P_{therm}}{C_{heat}*\Delta T}$

With this flow you can calculate the pressure loss with the formula found here: http://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation - preferably in the pressure loss form. For such a small pipe diameter it's pretty safe to assume laminar flow, then you don't even need to check for the friction factor in a Moody diagram. If the hose goes mainly straight up, you can calculate just the pressure loss from the distance and ignore fittings, bends, etc for a first shot.

This is not a complete walkthrough, But I'm quite confident you find everything you need one link from the wikipedia page I linked.

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Thank you. There would not be a heating pump installed. I also feel that 16mm is very thin, but that is the standard. In fact, most homes run that thin plastic pipe all the way from the heating tank to the home with no insulation! At my last place I insulated the pipe myself. –  dotancohen Jul 9 '12 at 14:14
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