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

Fluids

DensityThe density ρ of an object is its mass per unit volume:

The unit for density is kg/m3

Material Density (kg /m3)Aluminium 2700Gold 19300Ice 917Water 1000Oil 800Air 1.29Helium 0.179

PressurePressure is force acting perpendicular to a surface divided by the area A over which the force acts.

Knives, scissors, needles, papercuts…Why are these items effective in cutting or puncturing?

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

Fbot

Derive an expression for 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?

A B C D

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 / 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?

Explain

Buoyant Force (FB)The pressure at the top surface is given by:

The pressure at the bottom surface is given by:

Archimedes’ PrincipleA fluid will apply a buoyant force to an object that is partially or completely immersed in it; the magnitude of the

If the FB > mobjectg,

If the mobjectg > FB (max),

Archimedes’ Principle & Density

If ρobject > ρfluid

If ρobject < ρfluid

If ρobject = ρfluid

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

A plastic cube that measures 2cm on each side has a density of 706kg/m3. It is connected by a string to the bottom of the tank filled with water.

b) Determine the acceleration of the plastic if the string is cut

a) Find the tension in the string.

A geologist finds a rock. He determines the weight of the rock to be 32.14N while its apparent weight is 25.77N when placed in water. What is the density of this rock?

A frog in a hemispherical pod finds that he just floats without sinking in a fluid of density 1.35 g/cm3. If the pod has a radius of 6.00cm and negligible mass, what is the mass of the frog?

 

QUESTIONS: An air-filled balloon is floating just at the surface of the water as shown with a solid weight hanging from it.

a) What is true between the weight of the system and the buoyant force on the system?

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 PrincipleAny change in pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and the closed walls.

Brakes, hydraulics, syringes, etc

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/in2.

Where does air pressure come from?

air30km

About 99% of atmosphere is below 30km (~20miles)

What is force on piece of paper sitting on table?

Archimedes’ Principle for Gases

This principle also works in the air; this is why hot-air and helium balloons rise.

BarometerA 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.

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

Atmospheric Pressure and Gauge Pressure

Most pressure gauges measure the pressure above the atmospheric pressure – this is called the gauge pressure.

A car tire is inflated to 35psi. Is that the gauge pressure?

ExampleEach of the four tires of a 1450-kg car have a gauge pressure of 221 kPa (32.0 lb/in2). How much area of each tire is in contact with the ground?

Pressure & BoilingThe lower the pressure on a liquid, the easier it is to make it boil, i.e., as pressure increases, so does the boiling pt.

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/cm3) in an aorta with cross sectional area 2.0cm2 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 Patm subtracted out.

When calculating P1 or P2 this is the ABSOLUTE pressure. To find GAUGE pressure, you need to subtract away Patm.

Pabs = Patm + Pgauge

*Note on Bernoulli equation

ExampleIf 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 335m2?

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.

Water circulates throughout a house in a hot-water heating system. The water is pumped out at a speed of 0.50m/s through a 4.0cm diameter pipe in the basement under a pressure of 3.0 atm. It proceeds 5.0m upwards to 2nd floor where it moves through a 2.6cm diameter pipe. a)Determine the flow speed in smaller pipe. b)Determine the gauge pressure in smaller pipe

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.