Thermal Expansion Pipes

Overview

Engineering reference data for Thermal Expansion Pipes in fluid mechanics.

Key Formulas

Reynolds Number

$Re = \frac{\rho v D}{\mu}$

Ratio of inertial to viscous forces — determines flow regime.

Bernoulli's Equation

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$

Conservation of energy for steady, inviscid, incompressible flow.

Continuity Equation

$A_1 v_1 = A_2 v_2$

Conservation of mass for incompressible flow.

Darcy-Weisbach

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Pressure drop due to friction in a pipe.

Variables

Symbol	Description	Unit
$Re$	Reynolds number	—
$\rho$	Fluid density	kg/m³
$v$	Flow velocity	m/s
$D$	Characteristic dimension	m
$\mu$	Dynamic viscosity	Pa·s
$P$	Pressure	Pa
$f$	Darcy friction factor	—

Unit Conversions

• Temperature: $\Delta T_{°C} = \frac{5}{9} \cdot \Delta T_{°F}$
• Length: $1 \text{ ft} = 0.3048 \text{ m}$
• Length: $1 \text{ in} = 25.4 \text{ mm}$

Calculation Example

Problem: A copper tube with length 35 m (115 ft) is heated from 20 °C (68 °F) to 60 °C (140 °F) — a temperature difference of 40 °C (71 °F).

Solution: From the table, the linear expansion for copper at 71 °F temperature change is approximately 0.13 m/100 m (1.6 in/100 ft).

Metric calculation:

$\Delta l = \frac{35 \text{ m} \times 0.13 \text{ m}}{100 \text{ m}} = 0.05 \text{ m}$

Imperial calculation:

$\Delta l = \frac{115 \text{ ft} \times 1.6 \text{ in}}{100 \text{ ft}} = 1.8 \text{ in}$

Interactive Charts

References

• Original Source