Internal flow is the transport of fluids in pipes, ducts and conduits (flow sections). There are different flow regimes for the flow of fluids: laminar flow, transitional flow, and turbulent flow. Flow regimes mainly depend on the ratio of inertial forces to viscous forces, with the ratio being called the Reynolds number. 

For non-circular pipes, the Reynolds number is based on the hydraulic diameter D_h.

Flow Regimes

For the different flow regimes in circular pipes, the Reynolds number is different (Figure 1): 

• Laminar flow, Re < 2300 – characterised by smooth streamlines and highly ordered motion. 

• Transitional flow, 2300 < Re < 4000 – flow switches between laminar and turbulent randomly.

• Turbulent flow, Re > 4000– characterised by velocity fluctuations and highly disordered motion.  

Entrance of Pipe Flow

The boundary layer is a region where the viscous shearing forces caused by fluid viscosity are felt. At the boundary layers hypothetical surface divides the flow into two areas (Figure 2) (Course hero, 2020): 

• The boundary layer region – a region of flow in which viscous effects and velocity changes are significant.
• Irrotational (core) flow region – frictional forces are negligible, and velocity remains constant in the radial direction. 

When the temperature profile is constant, the flow is fully developed, with hydrodynamically developed flow equivalent to fully developed flow.

For laminar flow, the velocity profile in the fully developed region is parabolic and somewhat flatter in the turbulent area (Figure 3). 

The hydrodynamic entry length is the distance from the pipe entrance to where the wall shear stress (and thus the friction factor) reaches within about 2% of the fully developed value (TEXSTAN, 2021). For laminar flow, the hydrodynamic entry length is given approximately when the temperature profile is unchanging (Figure 4). 

During turbulent flow, due to the intense mixing, random fluctuations dominate the effects of molecular diffusion. Thus, the hydrodynamic entry length is approximated: 

References

Course hero. (2020). MEC554 FLUID LAB 2 FLOW PAST CYLINDER. Retrieved from Course hero: https://www.coursehero.com/file/47519253/MEC554-FLUID-LAB-2-FLOW-PAST-CYLINDER-COMPILEpdf/

jaimeirastorza. (2017). transition laminar turbulent flow. Retrieved from jaimeirastorza: https://jaimeirastorza.wordpress.com/2017/03/17/elegance-in-flight-book-review/transition-laminar-turbulent-flow/

slidetodoc. (2020). Viscous flow in ducts Circular and noncircular ducts. Retrieved from slidetodoc: https://slidetodoc.com/viscous-flow-in-ducts-circular-and-noncircular-ducts/

TEXSTAN. (2021). TEXSTAN Glossary of Terms – definitions and explanations. Retrieved from TEXSTAN: http://texstan.com/glossary.php

Dr. Adam Zaidi

Dr. Adam Zaidi, PhD, is a researcher at The University of Manchester (UK). His doctoral research focuses on reducing carbon dioxide emissions in hydrogen production processes. Adam’s expertise includes process scale-up and material development.’

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What Pressure Is Involved In Driving Fluid Through Pipes And Fittings?

Pressure is force acted per unit area

Pressure in a pipeline may be due to pumping, vaporization, compression, etc. The fluid should travel the entire pipeline without losing its pressure otherwise we need to spend extra for pumping the fluid to compromise for the loss in pressure.

Why Is Pressure Lost Through Pipes?

The reason is due to friction, wake formation, separation of the boundary layer by fittings, pipe roughness, etc. In order for the pump to work efficiently, the pump will be designed to accommodate any extra pressure that is required.

Pressure drop due to unseparated boundary layers (Skin friction) can be calculated by the following classical formula,

Pressure drop varies with length and diameter of the pipe, velocity, and density of the fluid, and Fanning friction factor. Don’t confuse this fanning friction factor with Darcy’s friction factor.

The Fanning friction factor varies with the nature of the flow. So if we know the nature of flow i.e., laminar or turbulent we can calculate the ‘f ‘ value accordingly.

If the flow is laminar the fanning friction varies with Reynolds number as follows,

If the flow is turbulent a lot of equations are in practice and you can use any of those equations at the expense of accuracy. the equations are mentioned as follows.

• Colebrook equation (1938)

• Swamee and Jain equation (1976)

• Haaland equation. (1983)

The ‘ ε ‘ symbol corresponds to the roughness factor which depends on the material of the construction of the pipe, whereas D and Re have their usual meaning.

After calculating the friction factor, we can find the pressure drop due to skin friction in a pipeline by substituting the ‘ f ‘ value into the pressure drop formula stated earlier.

In the Second Part pressure drop due to fittings will be covered.

Hassan Ahmed

Hassan graduated with a Master’s degree in Chemical Engineering from the University of Chester (UK). He currently works as a design engineering consultant for one of the largest engineering firms in the world along with being an associate member of the Institute of Chemical Engineers (IChemE).

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