Fluids at Rest Pressure Pressure is the Force

Fluids at Rest: Pressure • Pressure is the Force per unit Area: (uniform force on flat area) (definition of pressure) 1 Pa = 1 N/m 2 • Standard Atmospheric Pressure: 1 atm = 1. 013× 105 N/m 2 = 1. 013× 105 Pa = 14. 7 lb/in 2 • Gauge Pressure: Equal to the absolute pressure minus 1 atm. • Pressure in a Fluid at Rest (density r): (pressure at depth y) R. Field 10/24/2013 University of Florida PHY 2053 1

Pascal’s and Archimedes’ Principles • Pascal’s Principle: Pressure applied to an enclosed fluid is transmitted undiminished to all parts of the fluid and to the walls of the container. • Archimedes’ Principle: Any body, wholly or partially submerged in a fluid, is buoyed up by a force equal to the weight, Mfg, of the displaced fluid. R. Field 10/24/2013 University of Florida PHY 2053 2

Fluids at Rest: Example • A hollow spherical iron shell floats almost completely submerged in water (i. e. just touching the surface). If the density of iron is a factor f greater than the density of water (i. e. riron = f × rwater) and if the outer radius of the iron shell is R 2, what is the inner radius R 1? R. Field 10/24/2013 University of Florida PHY 2053 3

Fluids at Rest: Examples • The U-tube shown in the figure contains a liguid of density r. What is the pressure difference DP = PA - PB? Manometer • The U-tube shown in the figure contains two liquids in static equilibrium: Water of density r. W is in the right arm, and an oil of unknown density r. X is in the left arm. What is the density of the unknown oil in terms of d and L? R. Field 10/24/2013 University of Florida PHY 2053 4

Exam 2 Fall 2011: Problem 36 • Two small balls are simultaneously released from rest in a deep pool of water (with density rwater). The first ball is reseased from rest at the surface of the pool and has a density three times the density of water (i. e. r 1 = 3 rwater). A second ball of unknown density is released from rest at the bottom of the pool. If it takes the second ball the same amount of time to reach the surface of the pool as it takes for the first ball to reach the bottom of the pool, what is the density of the second ball? Neglect hydrodynamic drag forces. Answer: 3 rwater/5 % Right: 22% R. Field 10/24/2013 University of Florida PHY 2053 5

Exam 2 Spring 12: Problem 46 • What is the minimum radius (in m) that a spherical helium balloon must have in order to lift a total mass of m = 10 -kg (including the mass of the empty balloon) off the ground? The density of helium and the air are, r. HE = 0. 18 kg/m 3 and rair = 1. 2 kg/m 3, respectively. Answer: 1. 33 % Right: 37% R. Field 10/24/2013 University of Florida PHY 2053 6