## B

Rather than solving for temperature drop, given the number of hours, the hours are determined based on hours to freeze =

available heat

Btu heat loss/ hr Btu/ hr where available heat is WCp At, with W= lb of water

At= t start

In calculation 2, the heat-loss value should be calculated based upon the minimum temperature at which the system should stay, for example, 35°F. The heat tracing should provide enough heat to the system to offset the naturally occurring losses of the pipe. Heat-trace calculations are quite complex and many variables are involved. References 8 and 10 should be consulted for this type of work.

Calculations 3 and 4 relate to Section 4.5.3, dealing with flows. In the case of water, the minimum temperature can beset at 32°F and the heat-transfer rate is again on an operating average temperature th =

The equations given can be manipulated to solve for flow rate or insulation thickness.

As an aid in estimating the amount of insulation for freeze protection, Table 15.7 shows both the hours to freezing and the minimum flow rate to prevent freezing based on different insulation thicknesses. These figures are based on an initial water temperature of 42°F, an ambient temperature of - 10°F, a surface resistance of 0.54, and a thermal conductivity for fiberglass pipe insulation of k = 0.23.

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