Physics 101: Lecture 24, Pg 1 Exam 2 : The average increased from 62 to 66 % !

Physics 101: Lecture 24, Pg 2 Physics 101: Lecture 24 Fluids: Pascal, Archimedes and Bernoulli l Today’s lecture will cover Textbook Sections è Archimedes Principle & Buoyancy è Pascal’s Principle è Fluids in motion: Continuity & Bernoulli’s equation Note: Everything we do assumes fluid is non-viscous and incompressible.

Physics 101: Lecture 24, Pg 3 Pascal’s Principle l Any change in pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and the enclosed walls. Consequence: Two pistons with area A1 and A2 at the same height at different ends of an enclosed fluid: F 2 = F 1 (A 2 / A 1 )

Physics 101: Lecture 24, Pg 4 Physics 101: Lecture 24 Archimedes Principle (summary) l Buoyant Force (B) è weight of fluid displaced è B =  fluid x V displ g è W = Mg =  object V object g è object sinks if  object >  fluid è object floats if  object <  fluid l If object floats…. è B=W è Therefore  fluid g V displ. =  object g V object è Therefore V displ. /V object =  object /  fluid

Physics 101: Lecture 24, Pg 5 Suppose you float a large ice-cube in a glass of water, and that after you place the ice in the glass the level of the water is at the very brim. When the ice melts, the level of the water in the glass will: 1. Go up, causing the water to spill out of the glass. 2. Go down. 3. Stay the same. CORRECT Concept Question B =  W g V displaced W =  ice g V ice   W g V Must be same!

Physics 101: Lecture 24, Pg 6 Concept Question Which weighs more: 1. A large bathtub filled to the brim with water. 2. A large bathtub filled to the brim with water with a battle-ship floating in it. 3. They will weigh the same. Tub of water Tub of water + ship Overflowed water CORRECT Weight of ship = Buoyant force = Weight of displaced water

Physics 101: Lecture 24, Pg 7 Lecture 24: Fluid Flow (summary) Mass flow rate:  Av (kg/s) Volume flow rate: Av (m 3 /s) Continuity:  A 1 v 1 =  A 2 v 2 i.e., mass flow rate the same everywhere e.g., flow of river For fluid flow without friction: Bernoulli: P / 2  v  gh 1 = P / 2  v  gh 2 A 1 P 1 A 2 P 2 v1v1 v2v2 