Pressure Loss Calculations
Pressure Loss or Head Loss in a pipe can be calculated if the fluid data and the flow rate are known and specific attributes of the pipe are known (such as inner diameter of the pipe, length of the pipe, and roughness of the pipe material). There are a number of different calculations that must be performed in order to determine the pressure loss in the pipe due to the frictional resistances of fluid flow.
Fluid Flow States
Fluids in motion are subjected to various resistance forces, which are due to friction. Friction may occur between the fluid and the pipe work, but friction also occurs within the fluid as sliding between adjacent layers of fluid takes place.
The friction within the fluid is due to the fluid’s viscosity. When fluids have a high viscosity, the speed of flow tends to be low, and resistance to flow becomes almost totally dependant on the viscosity of the fluid. This condition is known as ‘Laminar flow’.
Fluids which have a low viscosity are usually moved at higher velocities. The flow characteristics change, small eddy currents occur within the flow stream, and the friction between the pipe work and the fluid becomes a factor to be considered. This type of flow is known as ‘Turbulent flow’.
Fluid Viscosity
A fluid viscosity can be described by its Dynamic viscosity (sometimes called Absolute viscosity), or it’s Kinematic viscosity. These two expressions of viscosity are not the same, but are linked via the fluid density.
Kinematic viscosity = Dynamic viscosity / fluid density
Dynamic Viscosity
Water @ 20°C has a viscosity of 1.00 x 10 -3 Pa • s or 1.00 Centipoise
Water @ 70°F has a viscosity of 2.04 x 10 -5 lb •s/ft²
Kinematic Viscosity
Water @ 20°C has a viscosity of 1.004 x 10 -6 m /s² or 1.004000 Centistokes
Water @ 70°F has a viscosity of 10.5900 x 10 -6 ft /s²
Pipe Flow Expert has a database of viscosities and densities for common fluids.
Note: Many terms can be used to describe a fluid’s viscosity (its resistance to flow): Centipoise, Poise, Saybolt Universal (SSU), Saybolt Furol, Ford Cup No. 3, Ford Cup No.4, Redwood No.1, Degrees Engler, Zahn No.1, Zahn No.2 and Zahn No. 3 are some of the scales that have been used in the immediate past.
All of these scales have differing upper and lower values and are usually not directly related to each other. Some references may be found in text books which attempt to list equivalent values for these different methods of measuring viscosity.
Dynamic viscosity must be converted to its Kinematic viscosity equivalent before the viscosity value can be used to calculate Reynold’s numbers and hence friction factors.
It is very common today to express dynamic viscosity in centipoise.
one Centipoise = 1 mPa.s or 0.001 (kg/m) x s
The units of centipoise are: Force per unit area x Time
It is very common today to express kinematic viscosity in centistokes.
one Centistoke = 1 mm²/s or 0.000001 m²/s
The units of centistokes are: Length² / Time
Kinematic viscosity is simply: Dynamic viscosity / Mass density
Reynolds Numbers
Reynolds numbers (Re) describe the relationship between a fluid’s velocity, the internal pipe diameter and the fluid’s Kinematic viscosity.
Reynolds number = Fluid velocity x Internal pipe diameter / Kinematic viscosity
Note : Kinematic viscosity (not Dynamic viscosity) must be used to calculate Reynolds numbers.
It is generally accepted that the ‘changeover’ point between laminar flow and turbulent flow, in a circular pipe, occurs when the Reynolds number (Re) is approximately 2100.
i.e. Laminar flow occurs when the Re is less than 2100. Turbulent flow occurs when the Re is greater than 2100.
Friction Factors
Many formulas have been developed to model the resistance to the flow of fluids. The Hazen-Williams formula has been a popular method of estimating the head loss in piping systems for a number of years. However, this empirical formula will only give reasonable accuracy if the fluid is water at 60°F or similar.
The Hazen-Williams formula is therefore not useful in analyzing a complex pipe system.
The Colebrook-White formula may be used with confidence to calculate an accurate friction factor applicable to the turbulent flow of fluids. The Colebrook-White formula is applicable over a whole range of fluid densities and viscosities, provided that the fluid flow is turbulent.
The Colebrook-White formula:
1/sqrt(f) = 1.14 - 2 log10 [e/D + 9.35/(Re x sqrt(f))]
f = friction factor
e = internal roughness of pipe
D = internal diameter of pipe
Re = Reynolds number
Friction factors for turbulent flow calculated by Pipe Flow Expert are based on the Colebrook-White formula.
The friction factor for Laminar flow is calculated from f = 64/Re
Fluid Head Loss (resistance to flow)
The resistance to fluid flow is usually expressed in fluid head. This is the height of a column of fluid which would exert enough pressure on the fluid at the bottom of the column to make the fluid flow within the system.
If the level of fluid (fluid head) is increased in a supply container, the volume of fluid entering the system from the supply container will increase due to the increase in pressure (force).
Fluid head resistance can be calculated by using the Darcy-Weisbach formula.
h fluid = f (L/D) x (v ²/2g)
f = friction factor
L = length of pipe workD = inner diameter of pipe work
v = velocity of fluid
g = acceleration due to gravity
Fluid head loss calculated by our Pipe Flow Expert software is based on the Darcy-Weisbach formula.
Calculation of Head Loss through Pipe Fittings and Bends
The fluid head resistance through various pipe work fittings can be calculated if the ‘K’ factor of the fitting is known. Many manufacturers of pipe work fittings and valves publish ‘K’ factors for their products.
Fluid head loss of these fitting can be calculated from:
h fluid = ‘K’ x v ² / 2g
‘K’ = manufacturer’s published ‘K’ factor for the fitting
v = velocity of fluid
g = acceleration due to gravity
In many systems where pipe lengths are relatively long, the effect of the fitting losses may be considered to be minor losses, and could be ignored during initial assessment.
If a partially open valve is part of the design, the effect of the valve should always be considered as the valve loss may be large.
Our Pipe Flow Expert software has a database of valve and fittings ‘K’ factors and calculation wizards for:
gradual enlargements
gradual contractions
sudden enlargements
sudden contractions
rounded entrances
long pipe bends
For further information on this subject please refer to the Crane Technical Paper No. 410 - ‘Flow of Fluids through valves, fittings and pipe’.
Calculation of the Total Pressure Loss in the Pipe
The fluid head resistance can also be expressed a pressure.
Metric units:
bar = h fluid x p x g / 100000
h = head loss (m)
p = fluid density (kg/m³)
g = acceleration due to gravity (m/s ²)
Imperial units:
psi = h fluid x SG x 2.311
h = head loss (ft)
SG = specific gravity of the fluid
Summary of the Pressure Loss Calculation
The following steps must be carried out to determine the fluid head necessary to overcome the flow of the fluid through a pipe:
Calculate the Reynolds number
Determine if the flow is Laminar or Turbulent
Calculate the friction factor for either Laminar flow or Turbulent flow
Calculate the fluid head resistance to overcome the flow through the pipe work
Determine the ‘K’ factors for the fittings within the pipe work layout
Calculate the fluid head resistance to overcome the flow through the fittings
Calculate the total fluid head resistance that is present in the pipe.
