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Power cost of idle electric water heater
wrote:
wrote:
A larger tank should help, given a smaller surface to lose heat from...
Larger tanks have less surface?
Imagine you have a cube tank that's one cubic foot.
Its surface area is six square feet. Now you take
another identical tank, cut the bottom off it, cut the
top off the first, and weld them together. You've
doubled your volume to two cubic feet, but you've only
increased your surface area by four square feet: two
1-foot cubes stacked on top of one another have an
*external* surface area of 10 square feet, not 12.
If you have a cylindrical tank, the volume is given by
h * (? * r * r)
where r * r = 'r squared' (no exponents in plain text
font) and h is the height.
The surface area is two times the surface area of the
circle on the end, plus the surface area of the sides:
(2 * (? * r * r)) + (2 * ? * r * h)
where the surface area of the sides is given by the
circumference of the cylinder's base, 2 * ? * r, times
the height.
If you now double the height of your cylinder, which
obviously doubles the volume, you can see that only the
expression to the right of the '+' sign in the formula
for the surface area is increased; 'h' doesn't appear
in the term to the left of the '+', meaning that as
height increases, that term is constant.
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