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This was a question posed to me by a homeowner. I don't know very much thermodynamics and hope someone here might have a better understanding.

They have a run of 3/8in copper pipe leading from their water heater to various taps. On cold mornings, it takes a long time, for hot water to flow to the faucets and shower heads. Their idea is to do a rough cost analysis to try and justify the cost of replumbing (making shorter run) from water heater to taps.

I thought a reasonable place to start is to calculate the heat lost along their run of pipe (perhaps in BTU/ft-hr). I found some information about this ref a. The Heat Transfer calculation assumes you know the temperature on both the inside and outside surface of the pipe. I could plug in some numbers for inside temperature; such as 130 deg F at the heater and 120 deg F by the time it reaches the tap (with assumption that the hot water temperature deceases along the run of pipe). I don't have any figure to use for the outside pipe surface temperature.

There is also a parameter

Perhaps there is an easier approach to this part of the question. One online ref b, with some

Your thoughts or suggestions are appreciated.

They have a run of 3/8in copper pipe leading from their water heater to various taps. On cold mornings, it takes a long time, for hot water to flow to the faucets and shower heads. Their idea is to do a rough cost analysis to try and justify the cost of replumbing (making shorter run) from water heater to taps.

I thought a reasonable place to start is to calculate the heat lost along their run of pipe (perhaps in BTU/ft-hr). I found some information about this ref a. The Heat Transfer calculation assumes you know the temperature on both the inside and outside surface of the pipe. I could plug in some numbers for inside temperature; such as 130 deg F at the heater and 120 deg F by the time it reaches the tap (with assumption that the hot water temperature deceases along the run of pipe). I don't have any figure to use for the outside pipe surface temperature.

There is also a parameter

**k**, the thermal conductivity, which is puzzling. In*Marks' Standard Handbook for Mechanical Engineering*, there is a table of Thermal Conductivity of Metals. For copper between 7 and 700 deg F, [itex]k_{to}= 232[/itex] and [itex] a = 0.032 [/itex]. In caption it states [itex] kt = kt_o - a(t-t_o)[/itex] and**k**(Btu/hr/ft^2/deg F/ft). The units are different from the**k**in ref2 which are Btu/hr-ft-deg F. They differ by units of ft^2 in denominator. Now if [itex] kt = kt_o - a(t-t_o)[/itex] , with a little algebra, I find that [itex]k = -a[/itex]. But that doesn't seem right either, because this value of [itex]a = 0.032[/itex] is 4 orders of magnitude from the thermal conductivity (108 Btu/hr-ft-deg F) of stainless steel used in example in ref2.Perhaps there is an easier approach to this part of the question. One online ref b, with some

*hand waving*, state the heat losses from a couple different diameters of copper hot water pipe, with and w/o insulation. They assume a constant inside pipe temperature of 140 deg F and mention the ambient air temperature is 70 deg F. I don't know if there may be standard tables to obtain this sort of information for the heating and plumbing industry.Your thoughts or suggestions are appreciated.

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