Head Loss: What It Is and How to Calculate It

  • Head loss is the pressure loss over a distance of pipe due to viscous effects
  • Frictional losses and minor losses contribute to total head loss
  • The Darcy-Weisbach equation is the most common equation used to calculate major head losses in a pipe
  • The friction factor helps determine head losses by calculating the degree of roughness in a pipe

Head loss is potential energy converted into kinetic energy. Head loss is defined as the pressure loss due to viscous effects over a certain distance of pipe for an incompressible fluid, also including the additional losses accrued by fixtures etc. Head loss cannot be avoided in real fluids, and its importance is relative to the value of the total head. It is created by the friction between the walls of the pipe and the fluid, the turbulence that is caused whenever the flow is affected or redirected in any way by the piping entrance or exit, valves, pumps, fittings and flow reducers.

piezometer casing
Piezometer casing above ground. Source.

Frictional losses, unlike velocity losses are not negligible in system calculations. It is directly proportional to the square of the fluid velocity, length of the pipe and the term that represents the dimensionless fluid factor, known as the friction factor or the Darcy friction factor. Head loss is inversely proportional to the pipe’s diameter. Head loss is a loss of energy, but it is not the total loss of energy for the fluid. The total loss of energy is a result of the law of conservation of energy. In the real world, the loss of energy due to friction inside of a pipe brings about an increase in the internal energy (temperature) of the fluid.

Head Loss Equation

The Darcy-Weisbach equation is an empirical equation, and is one of the most flexible head loss equations for a segment of pipe. It is represented by the equation:

Δpmajor_loss = λ (l / dh) (ρf v2 / 2)

 where:

λ               = Darcy-Weisbach friction coefficient

dh             = hydraulic diameter (m, ft)

l               = pipe length (m, ft)

Δpmajor_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)

This head loss equation is valid for steady state, incompressible and fully developed flow. The friction coefficient depends on the flow, if it’s transient, turbulent and laminar and roughness of the inside of the duct or tube.

Friction Factor

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

Relative Roughness = ε/D

The Moody chart denotes what the value of the friction factor will be, depending on the relative roughness and the Reynolds number.

Frictional Head Loss

Darcy’s equation for head loss, which is a mathematical relationship, can be used to calculate frictional head loss. Darcy’s equation has two forms: the first calculates the losses in a system due to the pipe length.

Hydraulic Gradient

The hydraulic gradient is the particular point of elevation to where the water level would rise to if left exposed to atmospheric pressure (for example in piezometer tubes) along a pipe run. The difference between the elevations of both of the water surfaces in each of the successive tubes, separated by a length of pipe, represents the friction loss for that specific length of pipe.

If a pipe run is on a friction slope that is calculated, and corresponds to the cross section, roughness coefficient and rate of discharge, the hydraulic gradient is parallel to the top of the conduit.

Hydraulic Head

head pressure illustration: Water is pushed through from the top tank to the bottom basin by hydraulic head pressure
Water is pushed through from the top tank to the bottom basin by hydraulic head pressure. Source.

Hydraulic head (piezometric head) is a particular measurement of liquid pressure over a vertical datum. It is typically measured as a liquid surface elevation, at the bottom (entrance) of a piezometer. It can be calculated in an aquifer from the depth of water in a piezometer well, with specific information regarding the piexometer’s screen depth and elevation. It can also be measured in a column of water with a standpipe piezometer, using a common datum relative to the height of the water.

Minor Losses

Losses within pipes that are caused by elbows, bends,valves, joints etc. are sometimes referred to as minor losses or local losses. This is not technically correct as the majority of the time the value of the “minor” losses are greater than that of the frictional losses in the straight piping sections, as discussed in the previous section. Minor losses are generally measured experimentally. The resulting data, in particular for valves, are dependent on the specific part and the design that the manufacturer went with.

For turbulent flow minor losses, the head loss varies as the square of the velocity. Therefore a convenient way of addressing the minor losses in flow is in relation to the loss coefficient (k). Loss coefficient values for general situations and typical fittings can be found in most standard fluid dynamics handbooks. The second form Darcy’s equation is used to calculate the value of individual system components minor losses.

Head Loss in Water Pipelines

Water pipeline where the above equation applies
Water pipeline where this equation applies. Source.

Head loss along a pipeline can be designated by the following equation:

hi – iL

where

Hi = pipeline head loss, m

i   = unit length head loss (hydraulic gradient)

L  = pipeline length

When analysing the Darcy-Weisbach equation (most common head loss equation used to calculate major head losses in a pipe) some interesting relationships can be determined:

  • Head loss is cut by half (for laminar flow) when the fluid’s viscosity is also halved.
  • If the pipe length is doubled, the frictional head loss generated will also be twice that of the previous length.
  • The head loss is generally proportional to the square of the velocity, so if the velocity is doubled, the resulting head loss will increase by a factor of four from its previous value.
  • At constant pipe length and flow rate, head loss will alway be inversely proportional to the 4th power of diameter (also for laminar flow). If the diameter of a pipe was decreased by half, the head loss would increase by a factor of 16! This will be a significant head loss value, and explains why bigger pipes require a pump that has relatively little power.

Head Loss of Two-Phase Fluid Flow

Contrastingly to single-phase head loss, the prediction and calculation of two-phase head loss is a significantly more complex problem and the leading methods differ by some margin. Experimental data shows that the frictional pressure drop in two-phase flow is substantially more than a single-phase flow with the same conditions.

What is your experience with head loss? If you have anything to add please let us know with a comment below!

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