Example 6: Calculate pressure drop for flow of water through sudden expansion in Turbulent Flow

Background

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.

Description

In this example water is treated as an incompressible fluid flowing through a sudden expansion. The actual frictional losses in the sudden expansion are also considered in the light of the theoretical increase in pressure which would be predicted by application of the Bernoulli Equation for a change (decrease) in velocity.

Problem Reference

Coulson and Richardson's Chemical Engineering, Vol 1, 6th Ed, (1999), Page 88, Example 3.6

Fluid Details

 Fluid : Water Phase : Liquid (incompressible) Density : 1000 kg/m³ Viscosity : 0.001 Pa.s (1.0 cP) Flow rate : 7.2 m³/h

Pipe Details

 ID before expansion : 40.0 mm ID after expansion : 50.0 mm Expansion type : sudden Pipe length : 0.001 m (*)

(*) AioFlo does not allow a pipe to have a zero length. This very short length has no impact on the pressure drop and is only entered to overcome the data entry error checking built into AioFlo.

To be Calculated

The head loss due to friction in passing through the sudden expansion, and the net change in pressure considering the friction losses and the change in velocity head.

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

Comparison of Results

Calculated Item Reference AioFlo
Friction head loss 16.5 mm water 16.9 mm water

Discussion

The results above show very close agreement between the reference and AioFlo for the frictional head loss through the sudden expansion. However, it has to be pointed out that the frictional loss is only part of the story. If the Bernoulli Equation was applied to this problem it would assume that there were no frictional losses and that as the fluid decelerated in flowing from the 40 mm pipe to the 50 mm pipe the kinetic energy lost would be converted to pressure energy. In the real world the Bernoulli effect and the frictional losses have to be considered. The Bernoulli Equation would predict that as the velocity decreased from 1.592 m/s to 1.019 m/s the velocity head would decrease by 76.4 mm water and the pressure would increase by the same amount. The frictional losses caused by the sudden expansion have been calculated as 16.9 mm water, making the net change an increase in pressure of 59.5 mm water (=76.4-16.9).

Unfortunately most texts on fluid mechanics discuss these two effects separately and do not always make it clear that both have to be considered at the same time. An interesting discussion of this topic occurred some time back on the Eng-Tips forum.