Unit 1: Fluid Dynamics An Introduction to Mechanical Engineering: Part Two Fluid dynamics Learning 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.

Unit 1: Fluid Dynamics An Introduction to Mechanical Engineering: Part Two 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.

Unit 1: Fluid Dynamics An Introduction to Mechanical Engineering: Part Two 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. Unit 1: Fluid Dynamics An Introduction to Mechanical Engineering: Part Two

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 Unit 1: Fluid Dynamics An Introduction to Mechanical Engineering: Part Two

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. Unit 1: Fluid Dynamics An Introduction to Mechanical Engineering: Part Two

1.5 Flow through pipes and ducts – key points By the end of this section you should have learnt that: 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 Unit 1: Fluid Dynamics An Introduction to Mechanical Engineering: Part Two

1.5 Flow through pipes and ducts – key points when the pipes and ducts are not circular, we can use the hydraulic diameter D h 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. Unit 1: Fluid Dynamics An Introduction to Mechanical Engineering: Part Two

1.6 Dimensional analysis in fluid dynamics – key points By the end of this section you should have learnt that: 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 Unit 1: Fluid Dynamics An Introduction to Mechanical Engineering: Part Two

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