Example 2: Pressure drop for Laminar Flow in pipe and fittings


The examples provide a comparison of AioFlo results with published data from well known and respected references that are generally accessible to engineers. This will allow prospective AioFlo users to validate its accuracy against a range of typical calculations. The worked examples can also be run by new users as part of their learning process. To learn more about AioFlo click on "Home" in the menu above.


This example retains the focus on Laminar Flow as in Example 1, but it extends the scope by including some pipe fittings and a change in elevation. The entrance and exit effects are still excluded.

Problem Reference

Flow of Fluids through Valves, Fittings, and Pipe. 1999, Crane Co., TP410M, Page 4-5, Example 4-9

Fluid Details

Flow rate : 2300 liter/minute
Phase : Liquid (incompressible)
Density : 899 kg/m
Viscosity : 450 centipoise

Pipe Details

Inside diameter : 128.2 mm (5.05")
Roughness : Not required
Straight length : 85 m
Elevation change : +15 m
Fittings : 1 x gate valve
1 x angle globe valve
1 x weld elbow (r/d=1)

To be Calculated

The total pressure drop over the system, as well as the individual pressure drops due to the straight pipe, the fittings and the change in elevation.

Download Link

You can run this example in AioFlo by downloading and opening the data file.

Comparison of Results

Calculated Item Reference AioFlo
Reynolds Number 760 760.6
Flow Regime Laminar Laminar
Pressure Drop, total (bar) 3.64 3.756
Pressure Drop, pipe (bar) 2.21 2.212
Pressure Drop, fittings (bar) 0.113 0.222
Pressure Drop, elevation (bar) 1.322 1.322


The AioFlo and Reference results look very close, but careful scrutiny is required to see the problem area. As mentioned in the Discussion of Example 1, the pressure drop due to friction in straight pipe can be solved analytically and of course the pressure drop due to change in elevation can also be solved analytically. It is therefore not surprising that there is close agreement for these two parameters.

While the pressure drops calculated for the fittings are fairly close in absolute terms, they are different by a factor of almost 2. When the resistance coefficients (K values) for the elbows and valves are scrutinized more closely it becomes evident that the Crane solution uses the values calculated for fully developed Turbulent Flow, and assumes that they do not change for Laminar Flow. AioFlo uses the Darby 3K method to calculate the fitting resistance coefficients, and this method takes the Reynolds Number into account. In this particular example the differences in the calculated pressure drops are masked by the much larger pressure drops due to the pipe friction and the elevation change, However, under different circumstances these errors could be significant. The question of how resistance coefficients vary in Laminar Flow will be examined further in Example 3

AioFlo showing Input Data and Results for Example 2

AioFlo running Example 2