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ME 101: Fluids Engineering Chapter 6 1 ME-101 Two Areas for Mechanical Engineers Fluid Statics – Deals with stationary objects • Ships, Tanks, Dams – Common calculations: • Pressure • Buoyancy Fluid Dynamics – Either fluid or object is in motion – Calculations include: • Flow Rate, Velocity, Drag Force, Lift Force, etc. 2 ME-101 Mechanical Engineers • Typical fluids – Water, Air, Oil, Nitrogen, Coolants, etc. • Why is it important? – 98% of electricity in US is generated by some form of fluid process (hydroelectric, steam turbines, wind) – Aeronautics – Biomedical 3 ME-101 What is a Fluid? Substance unable to resist a shear force without moving – Deforms continuously when subjected to a shear stress – Motion continues until force is removed Flow – Response of a fluid to shear stress that produces a continuous motion 4 ME-101 Two types of Fluids • A liquid is an incompressible fluid – Water, Oil, Coolants, Gasoline, etc. • A gas can be easily compressed – Air, Nitrogen, Propane, etc. 5 ME-101 Properties of Fluids What is a fluid shear force? Example: Consider a deck of cards Top card moves the most, bottom card is stationary – No-slip at solid-fluid boundary – stationary – Each layer moves at different speed 6 ME-101 Newtonian Fluid F A Applied force balanced by shear stress exerted by the fluid on the plate v h 7 ME-101 Viscosity v h - measure of friction or resistance to shear force Honey has higher viscosity than water Often see cP (centipoise) Water = 1cP at Room Temperature 8 kg 1 P 0. 1 m s ME-101 What happens when fluids interact with solids? The forces created are known as buoyancy, drag, and lift – Buoyancy is the force developed when a solid object is immersed in a fluid (no relative motion) – Lift and Drag forces arise when fluids interact with a solid object (relative motion) 9 ME-101 Why Does Pressure Increase with Depth? Pressure grows in direct proportion to the depth and density of the fluid p1 A po A hAg p1 po gh 10 ME-101 Buoyancy FB W fluid gVobject W FB Buoyancy force is related to the weight of the fluid displaced 11 ME-101 Laminar and Turbulent Flows Laminar Flow Turbulent Flow Irregular flow pattern – fluid moving fast, flow patterns break up, become random Fluid flows smoothly – associated with slow moving fluids (relatively) 12 ME-101 What determines laminar or turbulent flow? • Must consider the following: – Size of object moving through fluid (or size of pipe/duct fluid is flowing through) – Speed of object (or of fluid) – Density and viscosity of fluid • Exact relationship among these variables discovered by British engineer Osborne Reynolds • Reynolds number – Dimensionless parameter describes that transition 13 ME-101 Reynolds Number – l is a characteristic length – pipe diameter, diameter of sphere, diameter of air duct, etc. – ν is velocity – ρ is density – µ is viscosity vl Re Ratio between the inertia (density related) and viscous forces (viscosity related) acting within a fluid – When fluid moves quickly or is not very viscous or dense, Re large, inertia disrupts the flow – turbulent – When fluid is slow, very viscous, or very dense, Re is small, viscous effects stabilize the fluid – laminar 14 ME-101 Reynolds Number Flow is turbulent when Re > 4000 Flow is laminar when Re<2000 Experiments and detailed computer simulations necessary to understand complexity of fluids flowing in real hardware at real operating speeds 15 ME-101 Dimensionless Numbers • Reynolds Number vl Re L • Poisson’s Ratio d d L • Mach Number Ma speed of object (or fluid) speed of sound (or information) v L /T c L /T 16 ME-101 Pipe Flow • Fluids flow from high pressure to low pressure • Flow develops shear stress at boundary • Shear stresses balance pressure differential 17 ME-101 Laminar Pipe Flow Laminar velocity distribution for any point across the cross-section: Re < 2000 r 2 v vmax 1 R vmax d 2 p 16 L 18 ME-101 Pipe Flow Volumetric flow rate, q (volume/time) – Often more interested in knowing the volume of fluid flowing through a pipe during a certain time interval For steady, incompressible, laminar flow, the volumetric flow rate in a pipe is: d p q 128 L 4 19 ME-101 Volumetric Flow Rate Conservation of Mass – Incompressible Fluid V1 V2 A1v1 A2v2 20 ME-101 Aerodynamic Forces For straight and level flight: Lift = Weight Thrust = Drag 21 ME-101 Drag Force 1 FD Av 2CD 2 • Resists high-speed motion through fluid (air or water) • CD quantifies how streamlined an object is • Valid for any object or flow • Drag force is parallel to direction of fluid flow 22 ME-101 Lift Force 1 FL Av 2C L 2 • Lift due to pressure differences between upper and lower surfaces • Lift force increases with increasing angle of attack • Lift force is perpendicular to direction of fluid flow 23 ME-101 Airplane Wing – Turbulent Flow Stall Condition 24 ME-101