The Continuity Equation

2.1 Introduction

· Differential formulation of basic laws:

· Conservation of mass

· Conservation of momentum

· Conservation of energy

2.2 Flow Generation

(i) Forced convection. Motion is driven by mechanical means.

(ii) Free (natural) convection. Motion is driven by natural forces.

2.3 Laminar vs. Turbulent Flow

· Laminar flow: no fluctuations in velocity, pressure, temperature, …

· Turbulent flow: random fluctuations in velocity, pressure, temperature, …

· Transition from laminar to turbulent flow: Determined by the Reynolds number:

Flow over a flat plate: clip_image002

Flow through tubes: clip_image004

clip_image006

2.4 Conservation of Mass: The Continuity Equation

2.4.1 Cartesian Coordinates

The principle of conservation of mass is applied to an element dxdydz

Rate of mass added to element – Rate of mass removed from element =

Rate of mass change within element

clip_image008(2.1)

Expressing each term in terms of velocity components gives continuity equation

clip_image010

This equation can be expressed in different forms:

clip_image012

2.4.2 Cylindrical Coordinates

clip_image014

2.4.3 Spherical Coordinates

clip_image016

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