Nick, according to my calculations, there 5.3 cubic inches of water in
a foot of pipe, that is equal to .0229 gallons. At 8.33 pounds per
gallon, that is .191 pounds of water per foot of pipe. Assume 10 feet
of 3/4" pipe that sweats that is 1.91 pounds of water. To warm that
from 40 degrees incoming temperature to 70 degrees, at 1 BTU times 30
degrees times 1.91 pounds = 57.3 BTUs. At 8 cents per therm (100,000
BTUs) the cost savings gained by leaving the insulation off is.0045
cents every time you have to warm the water in the pipe. If the people
in the house use the water 40 times each day, the total savings per day
is .183 cents per day. Times 30 days per month is 5.49 cents (per
month). Nick, that is not enough to worry about. Even if you allow
for inefficiencies, it is still less than 10 cents per month. Nick,
that is not worth the time I just spent on it. Or do I need to write
that into a BASIC program to get the point across to you?

Stretch