Lecture 4 PDF

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Lecture 4:Properties of Fluids and Flows States of Matter Newton’s Laws Properties of Fluids Quiz Physical Properties of a Fluid Flow Regimes Boundary Layers Summary States of matter - Solids, liquids and gases are composed of molecules in continuous motion- The arrangements of the molecules and spa...

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Lecture 4: Properties of Fluids and Flows 1. States of Matter 2. Newton’s Laws 3. Properties of Fluids Quiz 4. Physical Properties of a Fluid 5. Flow Regimes 6. Boundary Layers 7. Summary 1) States of matter - Solids, liquids and gases are composed of molecules in continuous motion - The arrangements of the molecules and spaces between them differ, leading to the characteristic properties of the three different states of matter - Liquids and gases share a common characteristic in which they differ from solids: they are fluids; they flow under the action of a force, and deform continuously for as long as the force is applied 2) Newtons Law - Everything we can explain— forces that are act and forces we observe can be explained by Newtons laws - 1) A fluid will remain in rest or in a state of uniform motion in a straight line until acted on by an external force - 2) The rate of change of momentum of a fluid is proportional to the force applied and takes place in the direction of that force - 3) The magnitude and direction of a force and its reaction are equal and opposite - Newtons second law includes: F = ma where momentum is the product of mass (m) and velocity (u) so that for a fluid region of constant mass, Newton’s second law relates the change of velocity occurring in a given time (i.e. the acceleration) to the applied force F (known as the inertial force) - The dimensions come from the units - Need to understand position, velocity and acceleration and how they interact - velocity is a derivative for position and velocity is a derivative of acceleration

- Where forces are acted over a volume or area = pressure and stress - For a force that acts in a specific direction e.g. in the direction of the flow, the term stress is used, which is defined in a similar way to the pressure —-> stress = force / area

- In many cases the force exerted may vary from place to place on the boundary or fluid interface, it is convenient to work in terms of the pressure, p, acting in the fluid, acts equally in all directions —-> pressure = force / area 3) Physical of fluids quiz 1) Buoyancy — force that is associated with the materials being less dense to what its sitting on, causes an upwards force, need to work out the average density 2) Viscosity — how easy/hard it is to deform, concrete is more viscous than water as need more energy to deform it 3) Pressure associated with the weight of the fluid — e.g. water = hydrostatic pressure 4) Fluids move from areas of high pressure to areas of low pressure — e.g. toothpaste tube 4) Physical properties of a fluid - Mass density of a fluid is defined as the mass of fluid per unit volume = mass/ volume - Viscosity of a fluid is described as how ‘sticky’ a fluid is, need to quantity this by, speed of fluid at the boundary = speed of the boundary e.g. if stationary boundary, the fluid at the boundary will be stationary (no slip condition) - Velocity as you travel away from the boundary will increase - Didn't fluids provide different graphs depending on the viscosity of the fluid

- Shape of the curve is a measure of deformation

- Some net force must be

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driving this fluid in motion —-> gradient of velocity is a consequence of the stress that the boundary exerts on the moving fluid (and that the fluid exerts on the boundary; Newton’s third law). This stress acts in a direction parallel to the motion and so is called a shear stress The gradient of velocity is also called the strain rate as it has dimensions of strain (extension/ length) divided by time Deformation is described by the shear stress / gradient (strain rate) If direct relationship between each other = simple fluid / Newtonian fluids The effect of shear stresses can be related to the gradient of the velocity profile by a coefficient called the dynamic viscosity, which is a property of the fluid = shear stress / (du/dy) The study of fluid deformation is called rheology

5) Flow regimes - There are 2 different types of flow to exist - First demonstrated by Osbourne Reynolds experiment — simple high pressure to low pressure flow - Low speed of flow — also depends on the density, tube width and viscosity of fluid — dye didn't mix, motion looked smooth, had layers (laminae) — Laminar flow - High speed of flow — also depends on the density, tube width and viscosity of fluid — dye showed mixing across the fluid, more disordered, eddys occur within the fluid — Turbulent flow - Particle moving through a fluid — need to know if its a laminar flow or turbulent flow - Quantify if its turbulent or laminar is the Reynolds Number (Re) = - Re > 4000 can be assumed to be turbulent - Re > 2000 can be assumed as laminar...