Water at an average of 70F is flowing in a 2-in. steel pipe, schedule 40.
Steam at
220F is condensing on the outside of the pipe. The convective coefficient for the
water inside the pipe is h = 500 btu/hft 2F and the condensing steam coefficient on
the outside is h = 1500 btu/hft2F.
(a) Calculate the heat loss per unit length of 1 ft of pipe using resistances.
(b) Repeat, using the overall Ui based on the inside area Ai.
(c) Repeat, using Uo.
Ti = 70F
T0 = 220F
L = 1.0 ft
hi = 500 btu/hft2F (water)
ho = 1500 btu/hft2F (steam)
From Appendix 3-16
ksteel = 45.1 W/mk
ksteel = 45.1 W/mk ( 1.73073 ) = 26.06 btu/hft2F
From Appendix 5-1
For 2-in steel pipe Di = 2.067 in , Do = 2.375 in
ri = 1.0335 in , ro = 1.1875 in
Ai = 2Lri = 2(1.0ft)(1.0335 in/12) = 0.5421 ft2
Ao = 2(1.0ft)(1.1875 in/12) = 0.6218 ft2
Eq. (4.3-6)
Alm =
A o A i
Ao
ln
Ai
==
0.62180.5421
0.6218
ln
0.5421
Resistances
Ri =
1
hi A i
1
(500)(0.5421)
= 3.689x10-3
= 0.5810 ft2
RA =
r or i
kA A lm
Ro =
1
ho A o
(a) q =
(b) Ui =
1.18751.0335
26.06 (0.5810)(12)
1
(1500)(0.6218)
Ti
Ri + RA+ Ro
1
Ai R
q = UiAi( Ti
= 8.476x10-4
= 1.0722x10-3
70220
0.003689+ 0.0008476+0.0010722
1
(0.5421)(0.0056088)
= -26743.69 btu/h or
= 328.89 btu/hft2F or
= 328.89(0.5421)(70-220) = -26743.69 btu/h
q = 26743.69 btu/h
(c) Uo =
1
Ao R
q = UoAo( Ti
1
(0.6218)(0.0056088)
= 286.73 btu/hft2F
= 286.73(0.6218)(70-220) = -26743.69 btu/h
q = 26743.69 btu/h