Fluid FlowStreamlineFlow RateConservation of MassCanyonFluid EnergyBernoulli’s EquationLiftVenturi TubeFluid FlowFluid FlowStreamlineStreamlineMotion studies the paths of Motion studies the paths of objects.objects.Fluids motion studies many Fluids motion studies many paths at once.paths at once.The path of a single atom in The path of a single atom in the fluid is called a the fluid is called a streamlinestreamline..Flow RateFlow RateStreamlines can be grouped Streamlines can be grouped together.together.This corresponds to the fluid This corresponds to the fluid flow through an area.flow through an area.The flow rate measure fluid The flow rate measure fluid movement.movement.•mass per timemass per time•density times area times density times area times velocityvelocityAvFlowtmFlow /Conservation of MassConservation of MassLike other matter, fluids Like other matter, fluids cannot be created or cannot be created or destroyed.destroyed.The mass into a tube must The mass into a tube must flow out at the same rate.flow out at the same rate.This is called the This is called the continuity continuity equationequation..For constant density it only For constant density it only requires the area and requires the area and velocity.velocity.2211222111vAvAvAvACanyonCanyonA river flows in a channel A river flows in a channel that is 40. m wide and 2.2 m that is 40. m wide and 2.2 m deep with a speed of 4.5 deep with a speed of 4.5 m/s.m/s.The river enters a gorge that The river enters a gorge that is 3.7 m wide with a speed of is 3.7 m wide with a speed of 6.0 m/s. 6.0 m/s. How deep is the water in the How deep is the water in the gorge?gorge?The area is width times The area is width times depth. depth. AA11 = = ww11dd11Use the continuity equation.Use the continuity equation.vv11AA11 = = vv22AA22vv11ww11dd11 = = vv22ww22dd22Solve for the unknown Solve for the unknown dd22..dd22 = = vv11ww11dd11 / / vv22ww22(4.5 m/s)(40. m)(2.2 m) / (4.5 m/s)(40. m)(2.2 m) / (3.7m)(6.0 m/s) = 18 m(3.7m)(6.0 m/s) = 18 mFluid EnergyFluid EnergyThe kinetic energy in a fluid is the same as for any The kinetic energy in a fluid is the same as for any other mass: other mass: KK = ½ = ½ mvmv22..The change in potential energy is: The change in potential energy is: UU = mgh. = mgh.The work done on a fluid is due to pressure.The work done on a fluid is due to pressure.•Pressure acting on a volume: Pressure acting on a volume: WW = = PAPAx = PVx = PV..From the work energy principle:From the work energy principle:)()(1221222121yymgvvmVPVPUKWWoutinBernoulli’s EquationBernoulli’s EquationThe volume element is somewhat arbitrary in a The volume element is somewhat arbitrary in a moving fluid.moving fluid.•Mass divided by volume is densityMass divided by volume is density•Divide by volume and separate states on each end Divide by volume and separate states on each end 2221222121111221222121)()(vgyPvgyPyygvvPPBernoulli’s equation is equivalent to conservation of Bernoulli’s equation is equivalent to conservation of energy for fluids.energy for fluids.LiftLiftIf the height doesn’t change If the height doesn’t change much, Bernoulli becomes:much, Bernoulli becomes:Where speed is higher, Where speed is higher, pressure is lower.pressure is lower.Speed is higher on the long Speed is higher on the long surface of the wing – surface of the wing – creating a net force of lift.creating a net force of lift.2221221211vPvPFLVenturi TubeVenturi TubeA venturi meter uses A venturi meter uses continuity and Bernoulii’s continuity and Bernoulii’s equation to measure flow.equation to measure
View Full Document
Unlocking...