Physics 121: Lecture 21 Today,'s Agenda Announcements Homework 8: due Friday Nov. 11@ 6: 00 PM Chap.8:#7,22,28,33,35,44,45,50,54,61,and65 Today' s topics Fluids in motion Bernoullis equation Viscous fluids Simple oscillations Pendulum Physics 121: Lecture 21, Pg
Physics 121: Lecture 21, Pg 1 Physics 121: Lecture 21 Today’s Agenda Announcements Homework 8: due Friday Nov. 11 @ 6:00 PM. Chap. 8: # 7, 22, 28, 33, 35, 44, 45, 50, 54, 61, and 65. Today’s topics Fluids in motion Bernouilli’s equation Viscous fluids Simple oscillations Pendulum
Review: Fluids at rest What parameters do we use to describe fluids? Density Bulk modulus B △p (-△V/V) Pressure F=pAn A For incompressible fiuids(B>>p) p=const p(Ay )=Po+pgAy (y is depth) Pascals Principle Any change in the pressure applied to an enclosed fluid is transmitted to every portion of the fluid and to the walls of the containing vessel Physics 121: Lecture 21, Pg 2
Physics 121: Lecture 21, Pg 2 Review: Fluids at Rest What parameters do we use to describe fluids? Density Bulk Modulus Pressure For incompressible fluids ( ) Pascal’s Principle: Any change in the pressure applied to an enclosed fluid is transmitted to every portion of the fluid and to the walls of the containing vessel. ( V /V) p B − = B p = const. p(y ) = p0 + gy (y is depth) F = pAn ˆ A n
Archimedes' Principle( W,(W2? The buoyant force is equal to the difference in the pressures times the area B=(p2-p1)A=pg(y2-y1)A FB= Pliquidg Vliquid=Liquid.g=Wliq Archimedes The buoyant force is equal to the weight of the liquid displaced y1 The buoyant force determines whether an object will sink or float How does this work? Physics 121: Lecture 21, Pg 3
Physics 121: Lecture 21, Pg 3 The buoyant force is equal to the difference in the pressures times the area. W1 W2? FB = (p2 − p1 ) A = g(y2 - y1 )A FB liquidgVliquid Mliquid g = Wliquid = = Archimedes: The buoyant force is equal to the weight of the liquid displaced. The buoyant force determines whether an object will sink or float. How does this work? y 1 y 2 A p 1 p 2 F 1 F 2 Archimedes’ Principle
Fluids in Motion Up to now we have described fluids in terms of their static properties density p pressure p To describe fluid motion, we need something that can describe flow velocity v There are different kinds of fiuid flow of varying complexity non-steady / steady compressible incompressible rotational irrotational VISCOUS idea Physics 121: Lecture 21, Pg
Physics 121: Lecture 21, Pg 4 Fluids in Motion Up to now we have described fluids in terms of their static properties: density pressure p To describe fluid motion, we need something that can describe flow: velocity v There are different kinds of fluid flow of varying complexity non-steady / steady compressible / incompressible rotational / irrotational viscous / ideal
Ideal fluids Fluid dynamics is very complicated in general (turbulence, vortices, etc.) Consider the simplest case first the Ideal Fluid no" -no flow resistance(no internal friction) incompressible -density constant in space and time Simplest situation: consider streamline A ideal fluid moving with steady flow-velocity at each point in A the flow is constant in time In this case, fluid moves on streamlines Physics 121: Lecture 21, Pg 5
Physics 121: Lecture 21, Pg 5 Simplest situation: consider ideal fluid moving with steady flow - velocity at each point in the flow is constant in time In this case, fluid moves on streamlines A1 A2 v1 v2 streamline Ideal Fluids Fluid dynamics is very complicated in general (turbulence, vortices, etc.) Consider the simplest case first: the Ideal Fluid no “viscosity” - no flow resistance (no internal friction) incompressible - density constant in space and time