unit 1: fluid dynamics an introduction to mechanical engineering: part two fluid dynamics learning...

Unit 1: Fluid Dynamics

An Introduction to Mechanical Engineering: Part Two

Fluid dynamicsLearning summary

By the end of this chapter you should have learnt about:

• Basic concepts in fluid dynamics

• Boundary layers

• Drag on immersed bodies

• Flow through pipes and ducts

• Dimensional analysis in fluid dynamics.



1.2 Basic concepts in fluid dynamics – key points

By the end of this section you should have learnt that:• the Navier–Stokes equations are governing equations for

fluid motion, which can be derived from Newton’s second law of motion

• the continuity equation guarantees the conservation of mass

• the Reynolds number indicates a relative importance of inertial force in flow motion to viscous force

• the Froude number signifies the importance of inertial force in flow motion against the gravity force

• all flows become turbulent above the critical Reynolds number.



1.3 Boundary layers – key points

By the end of this section you should have learnt that:• viscous fluid does not slip at a solid wall surface. This

is called the non-slip condition of flow motion • the boundary layer is a thin fluid layer near a solid wall

surface, where the velocity is less than the freestream velocity

• the momentum thickness signifies the loss of momentum in the boundary layer due to skin-friction drag

• the displacement thickness is a measure of mass flow deficit in the boundary layer

1.3 Boundary layers – key points

• the boundary layer equations are a simplified form of the Navier–Stokes equations

• flow separation occurs over a curved surface when the static pressure increases in the flow direction.



1.4 Drag on immersed bodies – key points

By the end of this section you should have learnt that:

• pressure drag is a result of the boundary layer separation, where the static pressure difference is created between the front and rear of the bodies

• drag coefficient of immersed bodies is reduced with an increase in the Reynolds number when the flow is laminar

• drag coefficient of immersed bodies is suddenly reduced at the critical Reynolds number when the flow becomes turbulent



1.4 Drag on immersed bodies – key points

• surface roughness will reduce the critical Reynolds number of immersed bodies, thereby reducing their drag at lower Reynolds number

• streamlining is an effective strategy for reducing drag, where the immersed bodies are rounded at the front and tapered at the rear.



1.5 Flow through pipes and ducts – key points


• the friction factor of a pipe flow is a function of the Reynolds number and the surface roughness ratio, which can be obtained from the Moody chart

• whenever there are changes in velocity magnitude or direction in a pipe or duct system, there will be associated pressure drops, called minor losses

• the total head loss through the pipe system is obtained by adding the frictional head loss and all the minor losses



1.5 Flow through pipes and ducts – key points

• when the pipes and ducts are not circular, we can use the hydraulic diameter Dh to calculate the pipe losses

• the secondary flows in non-circular pipes and ducts are driven by the turbulent-shear stresses which act towards the corners of non-circular ducts.



1.6 Dimensional analysis in fluid dynamics – key points


• non-dimensional numbers are important in understanding the characteristics of the flow as well as in comparing the type of flow with others

• Buckingham’s theorem gives not only the number of non-dimensional quantities involved, but it also determines each non-dimensional quantity

• to carry out model tests, we need to ensure both the geometric and dynamic similarities are satisfied



1.6 Dimensional analysis in fluid dynamics – key points

• we can identify the shape of required pumps by calculating the specific speed without knowing the size of the pump.



unit 1: fluid dynamics an introduction to mechanical engineering: part two fluid dynamics learning...

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