KMEM4214 APPLIED VIBRATION

We are to define a fluid and how it differs between a solid and a gas.

In this book we look at an alternative way of deriving the governing equations of fluid flow using conservation of energy techniques on a differential element undergoing shear stress or viscous forces as it moves along a pipe and we use the expression for friction coefficient for laminar flow to derive the equations. We also derive a friction coefficient to work for Torricelli flow. We look at laminar, and turbulent flow. We look at cases where there is a pipe on a tank or an orifice and we develop the governing equations. We then develop a universal formula or equation that works for all types of flow i.e., laminar, transition and turbulen t flow in one equation. We go ahead and demonstrate Pouiselle flow and the conditions under which it will be observed. We explain other phenomena too.

Objectives • Introduce concepts necessary to analyse fluids in motion • Identify differences between Steady/unsteady uniform/non-uniform compressible/incompressible flow • Demonstrate streamlines and stream tubes • Introduce the Continuity principle through conservation of mass and control volumes • Derive the Bernoulli (energy) equation • Demonstrate practical uses of the Bernoulli and continuity equation in the analysis of flow • Introduce the momentum equation for a fluid • Demonstrate how the momentum equation and principle of conservation of momentum is used to predict forces induced by flowing fluids This section discusses the analysis of fluid in motion-fluid dynamics. The motion of fluids can be predicted in the same way as the motion of solids are predicted using the fundamental laws of physics together with the physical properties of the fluid. It is not difficult to envisage a very complex fluid flow. Spray behind a car; waves on beaches; hurricanes and tornadoes or any other atmospheric phenomenon are all example of highly complex fluid flows which can be analysed with varying degrees of success (in some cases hardly at all!). There are many common situations which are easily analysed. 3.1 Uniform Flow, Steady Flow It is possible-and useful-to classify the type of flow which is being examined into small number of groups. If we look at a fluid flowing under normal circumstances-a river for example-the conditions at one point will vary from those at another point (e.g. different velocity) we have non-uniform flow. If the conditions at one point vary as time passes then we have unsteady flow. Under some circumstances the flow will not be as changeable as this. He following terms describe the states which are used to classify fluid flow: • uniform flow: If the flow velocity is the same magnitude and direction at every point in the fluid it is said to be uniform. • non-uniform: If at a given instant, the velocity is not the same at every point the flow is non-uniform. (In practice, by this definition, every fluid that flows near a solid boundary will be non-uniform-as the fluid at the boundary must take the speed of the boundary, usually zero. However if the size and shape of the of the cross-section of the stream of fluid is constant the flow is considered uniform.) • steady: A steady flow is one in which the conditions (velocity, pressure and cross-section) may differ from point to point but DO NOT change with time. • unsteady: If at any point in the fluid, the conditions change with time, the flow is described as unsteady. (In practise there is always slight variations in velocity and pressure, but if the average values are constant, the flow is considered steady. Combining the above we can classify any flow in to one of four type: 1. Steady uniform flow. Conditions do not change with position in the stream or with time. An example is the flow of water in a pipe of constant diameter at constant velocity.

This textbook is designed for undergraduate students in mechanical or civil engineering and applied sciences. Assuming a background in calculus and physics, it focuses on using mathematics to model fluid mechanics principles. The book is organized into 13 chapters and uses both SI and British gravitational units. It includes a brief description of the engineering system and a discussion of gc for illustrative purposes.