PHYS 16 Lecture 29 Fluids Pressure and Buoyant

PHYS 16 – Lecture 29 Fluids: Pressure and Buoyant Force November 12, 2010

Review of Last Week…

Practice Question 1 • A black hole is an astronomical object that has a large mass concentrated at a single point. Given this information, what would be the escape velocity of a black hole? A) B) C) D) Undetermined Zero Infinity Proportional to √(M)

Practice Question 2 • A “day” on Mercury is very peculiar. It only takes Mercury from sunrise to noon (1/4 of a day) to sweep out half of it’s orbital area around the Sun. So how long must a day be? A) B) C) D) E) ¼ year ½ year 1 year 2 years 4 years

This Week • • Pressure and Pascal’s Principle Buoyant Force and Archimedes’ Principle Equation of Continuity Bernoulli’s Equation

Pressure

Liquid Pressure Varies with Depth • Find the pressure difference across a cube of water Would the pressure change be larger in salt water or fresh water? http: //www. open 2. net/open 2 static/source/file/root/0/30/19/124156/pressure_cube_b. jpg

Example: Container Height • If I start filling the following container with water, where will the highest water level be? Manoharan Lectures, Harvard University, Fall 2010

Example: Submarines • A submarine is submerged to a depth of 960 m. What air pressure is needed to blow water out of the ballast tanks? (density = 1024 kg/m 3) http: //www. yesmag. ca/how_work/submarine. html

Air Pressure Varies with Height • As height increases pressure decreases and density decreases http: //eo. ucar. edu/webweather/images/density. gif

Example Question: Pistons • Given that the density of air is proportional to pressure, how does the air pressure inside a confined volume change if the volume decreases by half? http: //www. tpub. com/fireman/25. htm Changes by 2…

Buoyant Force

Archimedes’ Principle • Buoyant force = the weight of the water displaced http: //www. open 2. net/open 2 static/source/file/root/0/30/19/124156/pressure_cube_b. jpg

Example: Buoyant force on objects 1) Buoyant force on brick in water -Volume= 0. 2 m X 0. 08 m X 0. 05 m -FB=8 N 2) Buoyant force on ball in water -Volume= (4/3)pi(0. 025)^2 -FB=0. 6 N 3) Buoyant force on Diet Coke vs. Coke -Volume= same in both cases -FB=same -Coke sinks more than Diet Coke bec. Coke more dense (Fgravity is more for Coke!)

Main Points • Pressure = Force/Area • Pressure varies with height • Buoyant force is equivalent to the weight of the water displaced