Fluids A fluid is anything that flows (liquid or a gas)

Density Material Density (kg /m 3 ) Aluminium2700 Gold19300 Ice917 Water1000 Oil800 Air1.29 Helium0.179

Pressure Pressure is force acting perpendicular

Pressure in Fluids Pressure is the same in every direction in a fluid at a given depth; if it were not, the fluid would flow….static equilibrium. How is pressure defined within a fluid?

Consider a beaker of water of area A and height, h. h The force exerted on top of water surface will be smaller than the force at bottom…why? Determine the weight of the water on top of bottom surface.

In which container would a fish experience more pressure from the liquid if the fish was at the bottom of each container? ABCD

Why doesn’t a giraffe’s brain explode when it drinks from a puddle or faint when it raises its head to such a large height above the heart? Pressure is height dependent above or below the heart.

Pressure / Density Questions 1. Why do swimmers float better in the ocean than in a lake? 2. Why don’t they make longer snorkels so that people could dive deeper without scuba gear? 4. When ice cubes melt when floating in water, does the water level rise, fall, or remain the same? 3. How do submarines change depth?

Atmospheric Pressure At sea level the atmospheric pressure is about 101.3kPa. This is called one atmosphere (1 atm). We also know this as 14.7 lb/in 2. Where does air pressure come from? 30km What is force on piece of paper sitting on table?

Atmospheric Pressure and Gauge Pressure Most pressure gauges measure the pressure above the atmospheric pressure – The absolute pressure is

Barometer A mercury barometer is used to measure atmospheric pressure. The height of the column of mercury is such that the pressure in the tube at the surface level is 1 atm.

Example A very long tube with a radius of 0.300cm is placed in a tightly fitting hole in the top of wine barrel with a radius of 20.0cm and filled to the lid with water. If water is filled in the tube to a height of 12.0m the barrel bursts. a) What is the mass of the water column in the tube? b) What is the net force on the lid of the barrel?

To what length could water be drawn up a vertical straw?

Pressure & Boiling

Buoyant Force (F B ) The pressure at the top surface is given by: The pressure at the bottom surface is given by:

Archimedes’ Principle Any fluid applies a buoyant force to an object that is partially or completely immersed in it; the magnitude of the If the F B > m object g If the m object g > F B (max),

Archimedes’ Principle & Density If ρ object > ρ fluid then object will sink. If ρ object < ρ fluid then object will float. If ρ object = ρ fluid then object can be anywhere in fluid (fish).

For a floating object, the fraction that is submerged is given by the ratio of the object’s density to that of the fluid.

Archimedes’ Principle for Gases This principle also works in the air; this is why hot-air and helium balloons rise. We have a buoyant force on us from the atmosphere.

A geologist finds a rock. He determines the mass of the rock to be 3.28kg while its apparent mass is 2.63kg when placed in water. What is the density of this rock?

QUESTIONS: An air-filled balloon is floating near the surface of the water with a solid weight hanging from it. a) What is true between the hanging weight and buoyant force on balloon? b) What if balloon is given a large shove downward and then let go. Describe the subsequent motion of balloon.

Consider a boat loaded with scrap iron in a swimming pool. If the iron is thrown overboard into the pool, will the water level at the edge of the pool rise, fall, or remain unchanged?

Pascal’s Principle Any change in pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and the closed walls.

Fluids in Motion

Equation of continuity The volume flow rate (Av) has the same value at every point along a tube that has a single entry and exit point for the fluid flow. For two positions…

Calculate the mass flow rate of blood (1.0g/cm 3 ) in an aorta with cross sectional area 2.0cm 2 if the flow speed is 0.40m/s. Example

Bernoulli’s Principle In steady flow for an incompressible fluid, the density ρ, the pressure P, the fluid velocity v and elevation y are related through

When a problem asks for gauge pressure, it wants the P atm subtracted out. When calculating P 1 or P 2 this is the ABSOLUTE pressure. To find GAUGE pressure, you need to subtract away P atm. P abs = P atm + P gauge Note on Bernoulli equation

Example If wind blows at 24.5m/s over the roof of a house, what is the NET force on the roof if it has an area of 335m 2 ? As wind blows over top, what happens to pressure on outside? Inside?

Application: Air moves faster over top of wing, slower beneath. This leads to lower pressure over wing and is one of factors that contributes to uplift of plane.

Application: Curve ball, air on one side of spinning ball faster than the other (leads to pressure difference)

Application: Atomizers, spray bottles, lawn sprayers

Determine an expression for the speed at which water leaves the tank which is a height h below the surface.