The hot water pipes in a house carry water from a boiler to the taps where the water is used. Heat is lost continuously through the sides of the pipes. If the pipes are lagged or insulated, this heat loss can be reduced.
Consider a pipe of inner radius
at temperature
and outer radius
at temperature
where
The rate of heat flow through the walls of the pipe is
where
is the cross sectional area of the pipe and
is the rate of flow of heat at the point where the radius is
If the pipe is thin so that
thenis approximately constant and equal to
and
hence
If the pipe contains
kg of water at temperaturethen then
and
so