# Modeling a Corrugated Pipe

**Modeling a Corrugated Pipe**

by Engineered Software, Inc.

Corrugated steel pipes, also called metal bellows and metal flexible hoses, are used extensively is piping application where flexibility is required due to vibration or thermal expansion. Determining the head loss of corrugated pipe was discussed by R. C. Hawthorne in the article "*Fluid Expansion Theory Computes Flow in Corrugated Hose*", published in Product Engineering, June 10th, 1963, pp 98-100. This article describes the R. C. Hawthorne's article and how to apply his methodology to model corrugated pipes in PIPE-FLO.

Hawthorne's key assertion in his article is that individual corrugates could be hydraulically represented as the flow expansion after an orifice, and the entire corrugated pipe can be represented as a series of uniformly spaced orifices. The Hawthorne model is shown in Figure 1.

**Figure 1.** Corrugated pipe showing the Pitch and Radial Expansion.

Hawthorne also states that the depth of the corrugation has little impact because the fluid quickly becomes nearly stagnant inside the valley. Instead, the distance between corrugations, or the **Pitch** (**S**), influences how much the fluid expands between corrugations, called the **Radial Expansion** (**r**).

Through testing, he was able to show that:

{r = 0.219 \times S} |

Hawthorne applied the Borda–Carnot equation for fluid expansion to each corrugation to determine the resistance coefficient K:

{K = \bigg[1-\bigg(\frac{D_1}{D_2}\bigg)^2\bigg]^2} |

Where:

D_{1} is the inside diameter of the corrugation.

D_{2} is the inside diameter of the sudden expansion.

Since the fluid expands in both directions,

{D_2 = D_1+2r} |

Substituting,

{D_2 = D_1+2(0.219S) = D_1+(0.438S)} |

The resistance coefficient, K, for each individual corrugatin becomes:

{K_{individual} = \bigg[1-\bigg(\frac{D_1}{D_1+(0.438S)}\bigg)^2\bigg]^2} |

To get the resistance coefficient for the entire length of the corrugated pipe, Hawthorne multiplied the individual resistance coefficient by the total number of corrugations, N:

{K_{Total} = N \bigg[1-\bigg(\frac{D_1}{D_1+(0.438S)}\bigg)^2\bigg]^2} |

The head loss of the corrugated pipe can then be calculated with the Darcy equation:

{H_L = K \frac{v^2}{2g}} |

The Fixed K value is the expansion coefficient equation times the number of corrugations.

{Fixed\ K = N \bigg[1-\bigg(\frac{D_1}{D_1+(0.438S)}\bigg)^2\bigg]^2} |

Applying Hawthorne's observations to a PIPE-FLO® model is simply done by calculating a **K** value for the corrugated pipe and adding this as a **Fixed K **value to a very short length pipe (ie: < 0.0001). The pipe size should be the size of the connecting solid pipeline.

For PIPE-FLO® Professional Version 12 and above, open the **Valve and Fittings dialog box** by selecting the pipe, clicking the **K (Valves & Fittings)** field in the **Property Grid**, expanding the **Other** category, and selecting **Fixed K**. Enter the K value, Description, Count, and Name (optional).

For Version 2009 and earlier, the **Valve and Fittings** tab is on the **Pipeline dialog box**.

Select to choose a **Fixed K** fitting and enter the calculated K value, Count, and Description.