# Pipe and Duct Systems - Total Head Loss

## Major and minor loss in pipes, tubes and duct systems.

The head loss of a pipe, tube or duct system, is the same as that produced in a straight pipe or duct whose length is equal to the pipes of the original systems plus the sum of the equivalent lengths of all the components in the system. This can be expressed as

h_{loss}= Σ h_{major_losses}+ Σ h_{minor_losses}(1)

where

h_{loss}= total head loss in the pipe or duct system

h_{major_losses}= major loss due to friction in the pipe or duct system

h_{minor_losses}= minor loss due to the components in the system

- Major Head Loss - head loss or pressure loss - due to friction in pipes and ducts.
- Minor Head Loss - head loss or pressure loss - due to components as valves, bends, tees and the like in the pipe or duct system.

### Summarized Major Losses

The major head loss for a single pipe or duct can be expressed as:

h_{major_loss}= λ (l / d_{h}) (v^{2}/ 2 g)(2)

where

h_{loss}= head loss (m, ft)

λ=Darcy-Weisbach friction coefficient

l= length of duct or pipe (m)

d_{h}= hydraulic diameter (m)

v= flow velocity (m/s, ft/s)

g= acceleration of gravity (m/s^{2}, ft/s^{2})

**Note!** - the head unit is with reference to the density of the flowing fluid. For other units - like *mm Water Column* - check Velocity Pressure Head.

### Summarized Minor Losses

Minor head loss can be expressed as:

h_{minor_loss}= ξ v^{2}/ 2 g(3)

where

Since the velocity - *v* - in equation *(2)* in general is related to the pipe or duct where the component is located, the sum of the minor losses in a pipe or duct can be expressed as:

Σ h_{minor_losses}= Σ ξ (v^{2}/ 2 g)(4)

The minor loss can be calculated by summarizing the minor loss coefficients - and multiplying the sum with the dynamic pressure head.

### Total Head Loss in a Single Pipe or Duct

The total head loss for a single pipe can be calculated by using equation *(1)* and *(3)*:

h_{loss_single}= λ (l / d_{h}) (v^{2}/ 2 g) + Σ ξ v^{2}/ 2 g(5)

or

h_{loss_single}= (λ (l / d_{h}) + Σ ξ ) (v^{2}/ 2 g)(6)

### Total Head Loss in Serial Connected Pipes

The total head loss in several serial connected pipes can be calculated by adding the total head loss in each pipe or duct. The total head loss can be expressed as:

h_{loss_serial}= Σ [(λ_{1}(l_{1}/ d_{h1}) + Σ ξ_{1}) (v_{1}^{2}/ 2 g) + .. + λ_{n}(l_{n}/ d_{hn}) + Σ ξ_{n}) (v_{n}^{2}/ 2 g)](7)for 1 to n serial connected pipes