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# Pipe and Duct Systems - Total Head Loss

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

### 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)

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

## Related Topics

### • Fluid Flow and Pressure Loss

Pipe lines - fluid flow and pressure loss - water, sewer, steel pipes, pvc pipes, copper tubes and more.

### • Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

## Related Documents

### Equivalent Length vs. Minor Pressure Head Loss in Pipe and Duct Components

Minor pressure and head loss in pipes vs. equivalent length in tubes and duct systems.

### Fluid Flow - Hydraulic Diameter

Calculate hydraulic diameter for pipes and ducts.

### Pipe and Tube System Components - Minor (Dynamic) Loss Coefficients

Minor loss coefficients for components used in pipe and tube systems.

Static pressure graphical presentation throughout a fluid flow system.

### Pressure Loss in Pipes connected in Series or Parallel

Calculate pressure loss in pipes connected in series or parallel.

### Pressure to Head Unit Converter

Pressure vs. head units - like lb/in2, atm, inches mercury, bars, Pa and more.

### Pumps - Head vs. Pressure

Converting head (ft or m) to pressure (psi or bar, kg/cm2) and vice versa.

### Pumps and Fans - Energy Equation and Head Rise

The energy equation can be used to calculate the head rise in pumps and fans.

### Steel Pipes Schedule 40 - Velocity Head vs. Water Flow

Velocity head can be used to calculate minor pressure or head loss in fluid flow systems.

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