Water Pipe Freeze Time

ScopeFrozen and burst pipes are the most common damage in a winter outage, and pipe insulation is widely believed to prevent them. It delays them. This calculator computes how long still water in a pipe in an unheated space has, in two stages per foot of pipe. First the water and the pipe wall cool to 32 degF exponentially, with a time constant of their heat capacity over the heat loss through the insulation, ln(r_out / r_pipe) / (2 pi k), in series with the outside air film. Then the water freezes at 32 degF, giving up 143.5 Btu per pound at a steady rate. It reports the onset and the time to freeze solid as bounds, since a pipe can block or split anywhere in between, and the same for the bare pipe. A 3/4 in type L copper line (0.875 in OD, 0.785 in ID, 0.455 lb/ft) with 1/2 in of foam (k 0.25) holding 55 degF water in a 0 degF crawl space carries 0.252 Btu/degF per foot and loses 0.139 Btu/h-degF per foot against 0.344 bare, about 59% less. It reaches 32 degF in about an hour and is frozen solid in 7.7 h, against 24 minutes and 3.1 h bare; at 20 degF it reaches 32 degF in 1.9 h and is solid in about 20 h. Insulation buys time for the power to return or for someone to drain the line; a dripping faucet is what prevents a freeze. It does not model moving water, heat from the structure or soil, wind, exterior-wall cavities, or supercooling, and it does not size heat trace (the Freeze-Protection Heat-Trace Cable and Circuit calculator). The plumber and the insulation manufacturer's data govern.

Formula or tableper foot: C = water lb/ft x 1.0 + pipe lb/ft x cp; UA' = 1 / (ln(r_out / r_pipe) / (2 pi k) + 1 / (h x 2 pi r_out)); t1 = (C / UA') x ln((T_start - T_amb) / (32 - T_amb)); t2 = water lb/ft x 143.5 / (UA' x (32 - T_amb)); onset t1 and solid t1 + t2 reported as bounds, with the bare pipe for comparison.

Source and editionSteady radial conduction through the insulation and an outside surface film, a lumped cool-down of the water and pipe wall, and the latent heat of fusion of water (143.5 Btu/lb) by name, with the ASHRAE Handbook -- Fundamentals chapter on insulation for mechanical systems cited by name for the freeze-time approach. Conductivity and surface coefficient are entered; the insulation manufacturer's data governs.

Free accessTextbook conduction and a latent-heat balance on the user's own pipe and insulation dimensions; no ASHRAE table or manufacturer chart is reproduced.

What governsEstimate. AHJ and licensed plumber / gas fitter govern. Verify against the IPC / IFGC edition adopted in your jurisdiction.

API field namespipe_od_in, pipe_id_in, pipe_lb_per_ft, pipe_cp_btu_per_lb_degf, insulation_thickness_in, insulation_k, surface_h_btuh_per_sqft_degf, water_start_degf, space_degf, water_lb_per_ft, heat_capacity_btu_per_degf_ft, ua_insulated_btuh_per_degf_ft, ua_bare_btuh_per_degf_ft, tau_insulated_hours, tau_bare_hours, onset_insulated_hours, freeze_stage_insulated_hours, solid_insulated_hours, onset_bare_hours, solid_bare_hours

• Still water, one pipe run no flow, no heat from the structure or soil, no supercoolingfreeze-time method, ASHRAE Handbook -- Fundamentals
• Latent heat of fusion of water 143.5 Btu/lbphysical data
• Water density 62.4 lb/cu ft for the water in the pipephysical data