© Pritchard Introduction to Fluid Mechanics Chapter 8 Internal Incompressible Viscous Flow

© Pritchard Main Topics Entrance Region Fully Developed Laminar Flow Between Infinite Parallel Plates Fully Developed Laminar Flow in a Pipe Turbulent Velocity Profiles in Fully Developed Pipe Flow Energy Considerations in Pipe Flow Calculation of Head Loss Solution of Pipe Flow Problems Flow Measurement

Internal Incompressible Viscous Flow

Turbulent flows Fluid particles rapidly mix as they move along due to random three-dimensional velocity fluctuations. Semi-empirical theories in conjunction with experimental data are the common approach for a turbulent flow. Computational solutions are also available through the use of some empirical parameters, however.

Turbulent flows in a duct

Turbulent flows

Incompressible flow

Velocity profiles for fully developed pipe flow

Energy Consideration in Pipe Flow

Use the empirical power- law profile, Eq

Head losses

Thermal energy converted from the mechanical energy from 1 to 2 Mechanical energies, pressure, kinetic, and potential energies.

Head losses

Calculation of Head Losses/Major Losses The mechanical energy loss is primarily due to the friction along a pipe and may be divided into two parts: Frictional loss along a straight,constant-flow-area pipe and frictional loss due to the change of flow area or path. The first part is called Major Loss and may be evaluated in terms of a horizontal pipe without the effect of elevation. The second part is called Minor Loss and will be discussed later.

Major losses GoogleGoogle images of roughness of a pipe

Major losses

Friction factor for turbulent flow Wall roughness affects the friction loss of turbulent flow. Since the wall roughness is random, an effective roughness is determined. sand size e

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Calculation of Head losses

© Pritchard Moody diagram

Calculation of friction factor

© Pritchard Heat losses due to flow area and pass changes/Minor Losses Minor Losses Examples: Inlets and Exits; Enlargements and Contractions; Pipe Bends; Valves and Fittings

© Pritchard Calculation of Head Loss Minor Loss: Loss Coefficient, K Minor Loss: Equivalent Length, L e

Calculation of Minor losses

Mechanical energy change of the fluid across the pump

The above equation is only for Mechanical energy change of the fluid across the pump, not a general energy balance!

Energy balance of a fluid system including a pump

The above equation may be rewritten as:

Thermal energy balance

Noncircular Ducts

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