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Pipe Expansion Thermal Loop Equations and Calculator

Fluids and Flow Design and Engineering

Pipe Thermal Expansion U Shape Loop Equations and Calculator for Pipe

Thermal expansion will occur between all fixed points in a piping system. If the system has the same covering height, natural fixed points will occur in the center of a line section between two expansion elbows. Unequal covering will cause the fixed point to be displaced due to varying frictional forces, and if there is any doubt, the fixed point should be set with an anchor. In all cases, this fixed point should be considered when calculating requirments for a pipe expansion loop.

Thermal Expansion U Shape Loop Equations and Calculator for Pipe

Δ L = c · L · ( Tf - Ta )

Loop Length

(W + 2H ) = [ ( 3 · E · D · Δ L ) / S ) ]1/2

Where:

ΔL = Thermal Expansion of known pipe length between fixed anchor points (in, mm),
c = Coefficient of expansion ( in/in °F, mm/mm °C ),
L = Distance between fixed anchor points (in, mm) ,
Tf = Temperature of fluid ( °F, °C ),
Ta = Temperature ambient (ground) to pipe ( °F, °C )
D = Diameter Outside of pipe (in, mm)
W = Width length of pipe (in, mm)
H = Height length of pipe (in, mm)
E = Modulus of elasticity (lb/in2, kPa)
S = Allowable stress in pipe (lb/in2, kPa)

* Keep units consistant (first units, second units)

Design Guidelines For Pipe Expansion Loop.

  • The expansion loop is usually located on the side of the hottest line.
  • The expansion loop, as a rule, should be located in the center of the distance between two anchors.
  • The height of the expansion loop is normally twice the width. The exception to this rule occurs when more than one line runs parallel in a common trench. The dimensions of the loops for the additional line must be increased to allow nesting of the loops.
Temp.
Thermal Expansion of Pipe
Inches per 100 ft.
mm per 100 meters
°F
Carbon Steel
Copper
Stainless
Steel
°C
–40
–0.288
–0.421
–0.461
–40
–24,0
–35,1
–38,4
–20
–0.145
–0.210
– 0.230
–28
–12,1
–17,4
–19,0
0
0
0
0
–17
0
0
0
20
0.148
0.238
0.230
–6
12,5
19,7
19,0
32
0.230
0.366
0.369
0
19,0
30,5
30,8
40
0.300
0.451
0.461
4
24,9
37,7
38,4
60
0.448
0.684
0.691
15
37,4
57,1
57,7
80
0.580
0.896
0.922
26
48,2
74,8
76,8
100
0.753
1.134
1.152
37
62,7
94,5
96,1
120
0.910
1.366
1.382
48
75,8
113,9
115,2
140
1.064
1.590
1.613
60
88,6
132,6
134,5
160
1.200
1.804
1.843
71
100,1
150,3
153,6
180
1.360
2.051
2.074
82
113,2
170,9
172,9
200
1.520
2.296
2.304
93
126,6
191,3
191,9
212
1.610
2.428
2.442
100
134,2
202,4
203,4
220
1.680
2.516
2.534
104
140,1
209,7
211,3
230
1.760
2.636
2.650
110
146,7
219,8
220,8
260
2.020
126
168,3
280
2.180
137
181,8
300
2.350
148
195,9
320
2.530
160
211,0
340
2.700
171
225,1
350
2.790
176
232,6

 

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