Fluid mechanics

FLUID MECHANICS

Game: The Foilboat Contest

Each group will construct a foilboat out of a 6” x 6” foil. The boat should support as many marbles as it can without sinking. The boat which can hold the most number of marble wins.

Why does a raft Why does a raft flow on water?flow on water?

Why is water Why is water turbulent in the turbulent in the rapids and rapids and smooth in other smooth in other places on a places on a river?river?

Defining a Fluid

• A fluid is a nonsolid state of matter in which the atoms or molecules are free to move past each other, as in a gas or a liquid.

• Both liquids and gases are considered fluids because they can flow and change shape.

• Liquids have a definite volume; gases do not.

Density

The concentration of matter of an object is

called the density.

ρ = mass

volume

The objects with lesser density than the

fluid where it is immersed will float.

Buoyant forces can keep objects afloat.

Have you ever wondered why things feel lighter underwater than they do in air?

Buoyant Force

The fluid exerts an upward force on objects that are

partially or completely submerged in it.

Displaced Volume of a Liquid

Apparent Weight Supports Buoyant Force Idea

Archimedes’ Principle determines

the amount of buoyancy.

Archimedes’ Principle

Any object completely or partially submerged in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid displaced by the object.

FB = Fg (displaced fluid) = mfgmagnitude of buoyant force = weight of

fluid displaced

Buoyant Force on Floating Objects

The density of an object determines the depth of submersion.

Buoyancy can be changed by changing

average density.

Conceptual Challenge

Astronauts sometimes train underwater to simulate conditions

in space. Explain why.

Explain why balloonists use helium instead of pure oxygen in balloons.

Sample Problem

A bargain hunter purchases a “gold” crown at a flea market. After she gets home, she hangs the crown from a scale and finds its weight to be 7.84 N. She then weighs the crown while it is immersed in water, and the scale reads 6.86 N. Is the crown made of pure gold? Explain.

Challenge: Eggsqueeze

Break the egg by simply squeezing it. Make sure you use

only one hand and wrap your fingers around the egg. You

must not wear rings.

Challenge: Floating Clips

Make a paper clip float in water.

Why do deep sea explorers have to wear diving suits?

Pressure

It is the magnitude of the force on a surface per unit area.

Pressure = Force Area

Unit

1 Pascal (Pa) = 1 N / m2

1atm = 1.013 x 105 Pa(atmospheric pressure at sea level)

Conversion to other units

1 bar = 100 000 Pa

1 torr = 133.32 Pa

1 psi = 6.894 x 103 Pa

Sample Problem

A force of 90 N is applied on a square surface with a length of 0.05 m. How much pressure is applied on the surface?

If the same amount of force is applied in a smaller square with a side equal to 0.025 m, how much pressure does it experience?

The Science of Toothpaste

Applied pressure is transmitted equally throughout a fluid.

Pascal’s Principle

The pressure applied to a fluid in a closed container is transmitted equally to every point of the fluid and to the walls of the container.

P1 = P2

F1 = F2

A1 A2

Sample Problem

The small piston of a hydraulic lift has an area of 0.20 m2. A car weighing 1.60 x 104 N sits on a rack mounted on the large piston. The large piston has an area of 0.90 m2. How large a force must be applied to a small piston to support the car?

Pressure varies with depth.

Water pressure

increases with depth because the water at a given depth

must support the weight of

the water above it.

Gauge Pressure

It is the pressure due to the weight of the column of liquid

on top of the object.

P = ρgh

Absolute Pressure

P = Po + ρgh

Absolute pressure = atmospheric pressure + gauge pressure

Atmospheric Pressure

It is the pressure from above.

Kinetic Theory of Gases can describe the origin of gas

pressure.

Sample Problem

Calculate the absolute pressure at an ocean depth of 1.00 x 103 m. Assume that the density of the water is 1.025 x 103 kg/m3 and that Po = 1.01 x 105 Pa.

Conceptual Challenge

A woman wearing snowshoes stands safely in the snow. If she removes her snow shoes, she quickly begins to

sink. Explain what happens in terms

of Force and Pressure.