ME 101: Fluids Engineering Chapter 6 ME-101 1

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. ME-101 2

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 ME-101 3

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 ME-101 4

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. ME-101 5

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 ME-101 6

Newtonian Fluid ME-101 Applied force balanced by shear stress exerted by the fluid on the plate 7

Viscosity ME-101  - measure of friction or resistance to shear force Honey has higher viscosity than water Often see cP (centipoise) Water = 1cP at Room Temperature 8

What happens when fluids interact with solids? ME-101 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

Why Does Pressure Increase with Depth? ME-101 Pressure grows in direct proportion to the depth and density of the fluid 10

Buoyancy ME-101 W FBFB Buoyancy force is related to the weight of the fluid displaced 11

Laminar and Turbulent Flows ME-101 Laminar FlowTurbulent Flow Fluid flows smoothly – associated with slow moving fluids (relatively) Irregular flow pattern – fluid moving fast, flow patterns break up, become random 12

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 ME

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 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 ME

Reynolds Number ME-101 Flow is turbulent whenRe > 4000 Flow is laminar whenRe<2000 Experiments and detailed computer simulations necessary to understand complexity of fluids flowing in real hardware at real operating speeds 15

Dimensionless Numbers Reynolds Number Poisson’s Ratio Mach Number ME

Pipe Flow Fluids flow from high pressure to low pressure Flow develops shear stress at boundary Shear stresses balance pressure differential ME

Laminar Pipe Flow Laminar velocity distribution for any point across the cross-section: ME-101 Re <

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: ME

Volumetric Flow Rate ME-101 Conservation of Mass – Incompressible Fluid 20

Aerodynamic Forces ME-101 For straight and level flight: Lift = Weight Thrust = Drag 21

Drag Force ME-101 Resists high-speed motion through fluid (air or water) C D quantifies how streamlined an object is Valid for any object or flow Drag force is parallel to direction of fluid flow 22

Lift Force ME-101 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

Airplane Wing – Turbulent Flow ME-101 Stall Condition 24