# Calculating Head Loss – Back to Basics

Potential energy converted into kinetic energy is a head loss. Head loss is characterized as pressure loss for an incompressible fluid due to viscous effects over a certain pipe span, including the additional losses accrued by fixtures, etc. Head loss in real fluids cannot be prevented and its meaning is proportional to the value of the total head. It is produced by the friction between the walls of the pipe and the fluid, the turbulence that is induced by the piping input or output, valves, pumps, fittings, and flow reducers if the flow is disturbed or diverted in some way.

Frictional losses in system measurements are not trivial, unlike velocity losses. It is directly proportional to the fluid velocity square, the pipe length, and the term representing the dimensionless fluid factor referred to as the friction factor or the friction factor of Darcy. Head loss is proportional inversely to the diameter of the tubing. Head loss is a loss of energy, but it is not the fluid’s total energy loss. The complete depletion of energy is a consequence of the law of energy conservation. The loss of energy in the real world due to friction within a pipe brings about an increase in the fluid’s internal energy (temperature).

## Equation for Calculating Head Loss

The Darcy-Weisbach equation is one of the most versatile head loss equations for a pipe section and is an empirical equation. It is portrayed by the equation:

*Δp _{major_loss} = λ (l / d_{h}) (ρf v^{2} / 2)*

* *where:

λ = Darcy-Weisbach friction coefficient

d_{h} = hydraulic diameter (m, ft)

l = pipe length (m, ft)

Δp_{major_loss} = friction pressure loss in fluid flow (Pa (N/m2), psf (lb/ft2))

ρf = fluid density (kg/m3, slugs/ft3)

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

For steady-state, incompressible, and fully formed flow, this head loss equation is valid. If it is transient, turbulent and laminar, the friction coefficient depends on the flow and the roughness of the interior of the duct or tube.

## Consider Friction Factor

For the degree of roughness of the inside surface of the pipe and the flow, the friction factor relies on the Reynolds number. Relative roughness is the sum used to measure the roughness of the pipe’s inner surface, divided by the diameter of the pipe, which is the average height of the surface imperfections (ε) (D).

Relative Ruggedness = ε/D

Depending on the relative roughness and the number of Reynolds, the Moody graph shows what the value of the friction factor would be.

## Determining Frictional Head Loss

To measure frictional head loss, Darcy’s equation for head loss, which is a mathematical relationship, can be used. There are two forms of Darcy’s equation: the first measures the losses due to the pipe length in a device.

### Assess the Hydraulic Gradient

The hydraulic gradient is the specific point of elevation to which the level of water will rise along a pipe run if left exposed to atmospheric pressure (for example in piezometer tubes). In each of the successive tubes, divided by a pipe length, the gap between the elevations of both the water surfaces reflects the lack of friction for that particular pipe length.

The hydraulic gradient is parallel to the top of the conduit if a pipe run is measured on a friction slope and corresponds to the cross-section, roughness coefficient, and discharge rate.

### Calculate Hydraulic Head

The hydraulic head (piezometric head) is a basic measurement of vertical liquid pressure. Usually, it is measured at the bottom (entrance) of a piezometer as a liquid surface elevation. In an aquifer, it can be measured from the depth of water in a piezometer well, with precise details on the screen depth and elevation of the piexometer. It can also be determined through a standpipe piezometer in a water column using a common date relative to the height of the water.

## Remember to Account for Minor Losses

Losses caused by elbows, twists, valves, joints, etc. inside pipes are often referred to as small losses or local losses. This is not theoretically true, since, as stated in the previous section, the importance of the “minor” losses is greater than that of the frictional losses in the straight piping sections most of the time. Minor losses are normally experimentally measured. The resulting data, especially for valves, depends on the specific component and the design of the manufacturer.

The head loss varies as the square of the velocity for small turbulent flow losses. Thus, with the loss coefficient, a convenient way to handle the small losses inflow is (k). In most basic fluid dynamics handbooks, loss coefficient values for general conditions and common fittings can be found. The second form of the Darcy equation is used to determine the value of minor losses for each device variable.

Head Loss in Water Pipelines

The following equation will specify head loss along a pipeline:

h_{i} – iL

where

H_{i} = pipeline head loss, m

i = unit length head loss (hydraulic gradient)

L = pipeline length

Some interesting relationships can be calculated when evaluating the Darcy-Weisbach equation (the most common head loss equation used to measure significant head losses in a pipe):

- When the fluid’s viscosity is also halved, the head loss is reduced by half (for laminar flow).
- If the length of the pipe is doubled, the induced frictional head loss will also be twice that of the previous length.
- The head loss is usually proportional to the square of the velocity, so the resulting head loss will increase by a factor of four from its previous value if the velocity is doubled.
- Head loss is often inversely proportional to the 4th power of diameter at constant pipe length and flow rate (also for laminar flow). The head loss would increase by a factor of 16 if the diameter of a pipe was reduced by half! This will be a significant value for head loss and explains why a pump that has relatively little power requires larger pipes.

## Two-Phase Fluid Flow – Head Loss

In comparison to single-phase head loss, a considerably more complicated issue is the estimation and measurement of two-phase head loss, and the leading methods vary by a certain margin. Experimental data show that in two-phase flow, the decrease in frictional pressure is significantly more than a single-phase flow with the same conditions.

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