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<br />G \J ';.. \.} u ~~ <br /> <br />OOPY:MCH <br /> <br />July 24, 1947 <br /> <br />Mr. Henry J. Hanzllk, <br />315 Cornell Avenue, <br />Swarthmore, Pennsylvanla. <br /> <br />My deer Mr. HanzUk: <br /> <br />Tour letter of June 23. 1947, to the offlce of the Chlef of the H1draulle <br />Laboratory regarding the free Bing of water ln penetocke of hydro-stat lone has <br />been referred to me for reply. <br /> <br />The Bureau has no publ1ehed U terature on th1e subject. however. the <br />followlng approximate formula has been developed here for estimatlng the time <br />required to freeze a plpe. It is: <br /> <br /> r- <br /> , <br />t = ~ / (b2 _ a2) I- K (b2 _ a2) <br />KT , II 2E <br /> i b <br /> - <br /> <br />7 <br />a2 loge (b) , <br />r tiiJ/ <br /> <br />In this expresslon <br /> <br />a repreeents the lnternal radius of the shell of ice <br /> <br />(feet) <br />(feet) <br /> <br />b the radius of the plpe <br /> <br />E the emisslvity oonstant expresslng the rate at whlch heat <br />wl11 be exchanged from the plpe Aurface to the <br />surroundlngs. Btu!(ft.)2(hr.)(01) <br /> <br />H the heat of fuslon of lce 143 Btu/lb. <br /> <br />K the oonductivity of lee 1.26 Btu/(ft. )(hr. )(oF) <br /> <br />t the tlme required to freeze a shell of lce <br />in to the radlus a (hours) <br /> <br />or the temperaturs dlfferential between the water ln the <br />plpe and the air temperature outside the plpe <br />(Rote that the water temperature ls assumed to be <br />3201 durlng the free Bing period.) <br /> <br />W the den81ty of water <br /> <br />(01) <br /> <br />62.4 lb./(ft.)3 <br /> <br />24 <br />