 # Problem Description

How do I solve headloss in a conduit using the Darcy-Weisbach friction method?

When using the Darcy-Weisbach friction method in gravity networks, how is the friction factor "f" solved for?

# Background

The storm-sewer products have a number of friction method options, including the Darcy-Weisbach equation. The Darcy-Weisbach equation includes a friction factor, f, which is solved by one of a couple of methods. The most common methods are the Swamee-Jain method and the Colebrook-While method.

The storm and sanitary OpenFlows products utilize the Swamee-Jain method. It should be noted that that the Colebrook-White method and the Swamee-Jain method yield the same results out to a certain level of precision, so you will likely see the same or similar results between the two methods.

A feature request has been filed with our developers so that a user can have the option of using either the Swamee-Jain or Colebrook-White methods. That will likely be available in a future release of the products.

# Solution

1. The user enters input data such as diameter and roughness height along with loading/inflows, and the flow is calculated for each pipe.

2. For a particular pipe, an initial guess is made for the upstream depth and the velocity corresponding to that depth is computed, based on the flow area (V = Q/A)

3. The Reynolds number is calculated based on that Velocity

4. The Swamee-Jain equation is then used to solve for the friction factor, f

5. The Darcy-Weisbach equation is then used to solve for the headloss

6. If the sum of the loss and downstream depth is not comparable to the upstream depth used in step 2, then steps 2-5 are repeated with a better guess of the depth.

7. The process ends when the depths are within the Hydraulic Grade Convergence Test value in the calculation options.

Equations used for Calculations

Reynolds number: Swamee-Jain: Darcy-Weisbach:

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