T1 - Essential Fluids - 2023.pptx

STEM Education & Design
Sep. 11, 2023
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
T1 - Essential Fluids - 2023.pptx
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T1 - Essential Fluids - 2023.pptx

Editor's Notes

  1. To appreciate energy conversion such as hydro, wave, tidal and wind power a detailed knowledge of fluid mechanics is essential. During the course of this lecture, a brief summary of the basic physical properties of fluids is provided and the conservation laws of mass and energy for an ideal (or inviscid) fluid are derived. The application of the conservation laws to situations of practical interest are also explored to illustrate how useful information about the flow can be derived. Finally, the effect of viscosity on the motion of a fluid around an immersed body (such as a turbine blade) and how the flow determines the forces acting on the body of interest.
  2. Density - Mass per unit volume of a fluid. For the purposes of this module, Density is assumed to be constant i.e. that the flow of the fluid is incompressible (small variations in pressure arising from fluid motion in comparison to atmospheric pressure). Pressure - Force per unit area, and acts in the normal direction to the surface of a body in a fluid. Its units are the pascal or N-m^2 Viscosity - Force per unit area due to internal friction in a fluid arising from the relative motion between neighbouring elements in a fluid. Viscous forces act in the tangential direction to the surface of a body immersed in a flow. (consider a deck of cards.
  3. Density - Mass per unit volume of a fluid. For the purposes of this module, Density is assumed to be constant i.e. that the flow of the fluid is incompressible (small variations in pressure arising from fluid motion in comparison to atmospheric pressure). Pressure - Force per unit area, and acts in the normal direction to the surface of a body in a fluid. Its units are the pascal or N-m^2 Viscosity - Force per unit area due to internal friction in a fluid arising from the relative motion between neighbouring elements in a fluid. Viscous forces act in the tangential direction to the surface of a body immersed in a flow. (consider a deck of cards.
  4. Density - Mass per unit volume of a fluid. For the purposes of this module, Density is assumed to be constant i.e. that the flow of the fluid is incompressible (small variations in pressure arising from fluid motion in comparison to atmospheric pressure). Pressure - Force per unit area, and acts in the normal direction to the surface of a body in a fluid. Its units are the pascal or N-m^2 Viscosity - Force per unit area due to internal friction in a fluid arising from the relative motion between neighbouring elements in a fluid. Viscous forces act in the tangential direction to the surface of a body immersed in a flow. (consider a deck of cards.
  5. Density - Mass per unit volume of a fluid. For the purposes of this module, Density is assumed to be constant i.e. that the flow of the fluid is incompressible (small variations in pressure arising from fluid motion in comparison to atmospheric pressure). Pressure - Force per unit area, and acts in the normal direction to the surface of a body in a fluid. Its units are the pascal or N-m^2 Viscosity - Force per unit area due to internal friction in a fluid arising from the relative motion between neighbouring elements in a fluid. Viscous forces act in the tangential direction to the surface of a body immersed in a flow. (consider a deck of cards.
  6. Density - Mass per unit volume of a fluid. For the purposes of this module, Density is assumed to be constant i.e. that the flow of the fluid is incompressible (small variations in pressure arising from fluid motion in comparison to atmospheric pressure). Pressure - Force per unit area, and acts in the normal direction to the surface of a body in a fluid. Its units are the pascal or N-m^2 Viscosity - Force per unit area due to internal friction in a fluid arising from the relative motion between neighbouring elements in a fluid. Viscous forces act in the tangential direction to the surface of a body immersed in a flow. (consider a deck of cards.
  7. Density - Mass per unit volume of a fluid. For the purposes of this module, Density is assumed to be constant i.e. that the flow of the fluid is incompressible (small variations in pressure arising from fluid motion in comparison to atmospheric pressure). Pressure - Force per unit area, and acts in the normal direction to the surface of a body in a fluid. Its units are the pascal or N-m^2 Viscosity - Force per unit area due to internal friction in a fluid arising from the relative motion between neighbouring elements in a fluid. Viscous forces act in the tangential direction to the surface of a body immersed in a flow. (consider a deck of cards.
  8. Density - Mass per unit volume of a fluid. For the purposes of this module, Density is assumed to be constant i.e. that the flow of the fluid is incompressible (small variations in pressure arising from fluid motion in comparison to atmospheric pressure). Pressure - Force per unit area, and acts in the normal direction to the surface of a body in a fluid. Its units are the pascal or N-m^2 Viscosity - Force per unit area due to internal friction in a fluid arising from the relative motion between neighbouring elements in a fluid. Viscous forces act in the tangential direction to the surface of a body immersed in a flow. (consider a deck of cards.
  9. Density - Mass per unit volume of a fluid. For the purposes of this module, Density is assumed to be constant i.e. that the flow of the fluid is incompressible (small variations in pressure arising from fluid motion in comparison to atmospheric pressure). Pressure - Force per unit area, and acts in the normal direction to the surface of a body in a fluid. Its units are the pascal or N-m^2 Viscosity - Force per unit area due to internal friction in a fluid arising from the relative motion between neighbouring elements in a fluid. Viscous forces act in the tangential direction to the surface of a body immersed in a flow. (consider a deck of cards.
  10. Density - Mass per unit volume of a fluid. For the purposes of this module, Density is assumed to be constant i.e. that the flow of the fluid is incompressible (small variations in pressure arising from fluid motion in comparison to atmospheric pressure). Pressure - Force per unit area, and acts in the normal direction to the surface of a body in a fluid. Its units are the pascal or N-m^2 Viscosity - Force per unit area due to internal friction in a fluid arising from the relative motion between neighbouring elements in a fluid. Viscous forces act in the tangential direction to the surface of a body immersed in a flow. (consider a deck of cards.
  11. Density - Mass per unit volume of a fluid. For the purposes of this module, Density is assumed to be constant i.e. that the flow of the fluid is incompressible (small variations in pressure arising from fluid motion in comparison to atmospheric pressure). Pressure - Force per unit area, and acts in the normal direction to the surface of a body in a fluid. Its units are the pascal or N-m^2 Viscosity - Force per unit area due to internal friction in a fluid arising from the relative motion between neighbouring elements in a fluid. Viscous forces act in the tangential direction to the surface of a body immersed in a flow. (consider a deck of cards.
  12. Density - Mass per unit volume of a fluid. For the purposes of this module, Density is assumed to be constant i.e. that the flow of the fluid is incompressible (small variations in pressure arising from fluid motion in comparison to atmospheric pressure). Pressure - Force per unit area, and acts in the normal direction to the surface of a body in a fluid. Its units are the pascal or N-m^2 Viscosity - Force per unit area due to internal friction in a fluid arising from the relative motion between neighbouring elements in a fluid. Viscous forces act in the tangential direction to the surface of a body immersed in a flow. (consider a deck of cards.
  13. A useful concept to visualize a velocity field is to imagine a set of streamlines para;;e; to the direction of motion at all points in the fluid. Any element of mass in the fluid flows along a notational stream-tube bounded by neighbouring streamlines. In practice, streamlines can be visualised by injecting small particles into the fluid e.g. smoke can be used in wind tunnels to visualise fluid flow around objects.
  14. Also known as conservation of mass. Consider flow along a stream tube in a steady velocity field. The direction of flow is parallel to the boundries and at any point within the stream tube, the speed of the fluid (u) and the cross-sectional area (A). Therefore the fluid is confined to the stream tube and the mass flow per second is constant. Therefore: Density * Velocity * Cross-sectional Area = Constant Therefore the speed of fluid is inversely proportional to the cross-sectional area of the stream tube.
  15. note the use of symbols here. DON’T confuse Volume (V) and velocity (V)
  16. For a stationary fluid, u = 0 everywhere in the fluid therefore this equation reduces to which is the equation for hydrostatic pressure. It shows that the fluid at a given depth is all the same at the same pressure.
  17. Consider the steady flow of an ideal fluid in the control volume shown. The height (z), cross sectional area (A), speed (u) and pressure are denoted. The increase in gravitational potential energy of a mass δm of fluid between z1 and z2 is δmg(z2-z1) In a short time interval (δt) the mass of fluid entering the control volume at P1 is δm=ρu1A1δt and the mass exiting at P2 is δm=ρu2A2δt
  18. In order for the fluid to enter the control volume it has to do work to overcome the pressure p1 exerted by the fluid. The work done in pushing the elemental mass δm a small distance δs = uδt at P1 is δW1= Pressure * Area * Distance moved = Pressure * Area * Velocity * Change in time. Remember F = P*A Similarly, the work done in pushing the elemental mass out of the control volume at P2 is δW2=-p2A2u2δt. The net work done is δW1+δW2
  19. Consider a liquid at a pressure p, moving with a velocity (u) at a height Z above datum level If a tube were inserted in the top of the pipe, the liquid would rise up the tube a distance of p/ρg and this is equivalent to an additional height of liquid relative to datum level. Etotal equation represents the specific energy of the liquid. Each of the quantities in the brackets have the units of length and are termed heads, i.e Z is referred to as the potential head of the liquid, p/ρg as the pressure head and V2/2g as the velocity head.
  20. Consider stations ① and ② of the inclined pipe illustrated. If there are no losses between these two sections, and no energy changes resulting from heat transfer of work, then the total energy will remain constant, therefore stations ① and ② can be set equal to one another, equ (1) If however losses do occur between the two stations, then equation equ (2) When energy is added to the fluid by a device such as a pump, or when energy is extracted by a turbine, these need also be accounted for equ (3). w is the specific work in J/kg NOTE - V1 and V2 indicated in diagram are u1 and u2 in derivation
  21. Consider the fluid flowing along the stream-line AB. In case (a), the fluid slows down as it approaches the stagnation point B. Putting u = U, p = po at A and u = 0, p = ps at B and applying bernoulli’s equation we get In example (and the previous question), ps is measured by tube (a) and p0 measured by tube (b). NOTE - ps is larger than p0 by an amount ps - p0 = ρU2. The quantities ρU2, p0 and ps = p0 + ρU2 are called the dynamic pressure, static pressure and total pressure respectively.
  22. The velocity profile is obtained by traversing the pitot tube along the line AA. The cross-section is divided into convenient areas, a1, a2, a3, etc... and the velocity at the centre of each area is determined
  23. A venturi meter is a device which is used to measure the rate of flow through a pipe. NOTE - V1 and V2 indicated in diagram are u1 and u2 in derivation
  24. An Orifice plate is another means of determining the fluid flow in a pipe and works on the same principle of the Venturi meter. The position of the Vena contract can be difficult establish and therefore the area A2. The constant k is determined experimentally when it will incorporate the coefficient of discharge. If h is small so that ρ is approximately constant then the this equation can be used for compressible fluid flow. NOTE - V1 and V2 indicated in diagram are u1 and u2 in derivation
  25. Let us consider a simple case of laminar flow between two parallel plates separated by a small distance d. The upper plate moves at a constant velocity U while the lower plate remains at rest. At the plate fluid interface in both cases there is no velocity due to the strong forces of attraction. Therefore the velocity profile in the fluid is given by
  26. Let us consider a simple case of laminar flow between two parallel plates separated by a small distance d. The upper plate moves at a constant velocity U while the lower plate remains at rest. At the plate fluid interface in both cases there is no velocity due to the strong forces of attraction. Therefore the velocity profile in the fluid is given by
  27. Let us consider a simple case of laminar flow between two parallel plates separated by a small distance d. The upper plate moves at a constant velocity U while the lower plate remains at rest. At the plate fluid interface in both cases there is no velocity due to the strong forces of attraction. Therefore the velocity profile in the fluid is given by
  28. Let us consider a simple case of laminar flow between two parallel plates separated by a small distance d. The upper plate moves at a constant velocity U while the lower plate remains at rest. At the plate fluid interface in both cases there is no velocity due to the strong forces of attraction. Therefore the velocity profile in the fluid is given by
  29. Let us consider a simple case of laminar flow between two parallel plates separated by a small distance d. The upper plate moves at a constant velocity U while the lower plate remains at rest. At the plate fluid interface in both cases there is no velocity due to the strong forces of attraction. Therefore the velocity profile in the fluid is given by
  30. Let us consider a simple case of laminar flow between two parallel plates separated by a small distance d. The upper plate moves at a constant velocity U while the lower plate remains at rest. At the plate fluid interface in both cases there is no velocity due to the strong forces of attraction. Therefore the velocity profile in the fluid is given by
  31. Let us consider a simple case of laminar flow between two parallel plates separated by a small distance d. The upper plate moves at a constant velocity U while the lower plate remains at rest. At the plate fluid interface in both cases there is no velocity due to the strong forces of attraction. Therefore the velocity profile in the fluid is given by
  32. Let us consider a simple case of laminar flow between two parallel plates separated by a small distance d. The upper plate moves at a constant velocity U while the lower plate remains at rest. At the plate fluid interface in both cases there is no velocity due to the strong forces of attraction. Therefore the velocity profile in the fluid is given by
  33. A viscous fluid can exhibit two different kinds of flow regimes, Laminar and Turbulent In laminar flow, the fluid slides along distinct stream-tubes and tends to be quite stable, Turbulent flow is disorderly and unstable The flow that exists in an y given situation depends on the ratio of the inertial force to the viscous force. The magnitude of this ratio is given by Reynolds number, where U is the velocity, L is the length and v = μ/ρ is the kinematic viscosity. Reynolds observed that flows at small Re where laminar while flow at high Re contained regions of turbulence
  34. For the inviscid flow the velocity fields in the upstream and downstream regions are symmetrical, therefore the corresponding pressure distribution is symmetrical. It follows that the net force exerted by the fluid on the cylinder is zero. This is an example of d’Alembert’s paradox For a body immersed in a viscious fluid, the component of velocity tangential to the surface of the fluid is zero at all points. At large Re numbers (Re>>1), the viscous force is negligible in the bulk of the fluid but us very significant in a viscous boundary layer close to the surface of the body. Rotational components of flow know as vorticity are generated within the boundary layer. As a certain point, the seperation point, the boundary layer becomes detached from the surface and vorticity are discharged into the body of the fluid. The vorticity are transported downstream side of the cylinder in the wake. Therefore the pressure distributions on the upstream and downstream sides of the cylinder are not symmetrical in the case of a viscous fluid. As a result, the cylinder experiences a net force in the direction of motion known as drag. In the case of a spinning cylinder, a force called life arises at right angles to the direction of flow.
  35. CL and CD are dimensionless constants know as the coefficient of Lift and the coefficient of Drag respectively. Lift and drag can be changed by altering the shape of a wing i.e. ailerons. For small angles of attack, the pressure distribution ont he upper surface of an aerofoil is significantly lower than that on the lower surface which results is in a net lift force.
  36. CL and CD are dimensionless constants know as the coefficient of Lift and the coefficient of Drag respectively. Lift and drag can be changed by altering the shape of a wing i.e. ailerons. For small angles of attack, the pressure distribution on the upper surface of an aerofoil is significantly lower than that on the lower surface which results is in a net lift force.