Pressure in Open Systems

• Pressure increases with depth

• Type of fluid also plays a role in pressure (more dense fluids will exert greater pressures)

• Gravity also plays a role (larger gravity results in larger pressure)

hgP

Pressure due to a liquid depends on DEPTH and Pressure due to a liquid depends on DEPTH and density, not volume!density, not volume!

Why is the water level the same in each vase?Why is the water level the same in each vase?

Which teapot can hold more tea?Which teapot can hold more tea?

Problem…

• A reservoir behind a dam is 15 m deep. What is the pressure of the water in the following situations?– At the base of the dam?– 5.0 m from the top of the dam?

• If the water were saltwater, would the pressures be greater or less?

Public Water System

Buoyancy

• What happens to water level when something is placed in it?

– It rises

• How much does it rise?– The amount of displaced water is equal to the volume of the

submerged part of the object

• A completely submerged object always displaces a volume of liquid equal to its own volume.

• This is a good way to find the volume of irregular shapes

Mr. Archimede’s Bath King Hiero’s Crown

Archimede’s Principle

• Greek scientist Archimede’s (212 B.C.) discovered that the “Buoyant force acting on an object placed in a fluid is equivalent to the weight of the displaced fluid”

• The force does not depend on the weight of the object, only the weight of the displaced fluid.

Buoyancy

• A buoyant force is an upward force exerted on objects when placed in a fluid, due to the difference in pressure between the bottom and top of an object– Magnitude of the force

depends on• Volume of displaced fluid

• Density of displaced fluid

• Magnitude of gravity

VgFb

1 liter of water = 1000 cm3 = 1 kg = 9.8 N1 liter of water = 1000 cm3 = 1 kg = 9.8 N

Flotation• What is the buoyant force on a 10 ton ship

floating in fresh water?

• In salt water?

• In a lake of mercury?• 10 tons in each case; the weight of the ship is

constant, so the weight of the water displaced must also be constant. The volume of the liquid displaced will differ based on the density of the liquid.

Flotation

• How can a ship be made of iron if a solid block of iron sinks?– It has to do with the shape of the ship

• Principle of Flotation—a floating object displaces a weight of fluid equal to its own weight– The ship must be shaped to displace enough water

to equal its own weight– The deeper the ship is immersed, the more water it

displaces—a loaded ship will ride lower in the water than an unloaded ship

Problem…

• A 10 lb box falls overboard a boat, and is now floating in the water. The box has the shape of a cube, 1 ft on a side. What is the buoyancy force on the box?

• How much of the box is under water? (assume it is floating level)

Problem…

• The float in a toilet tank is a sphere of diameter 10 cm.

• 1) What is the buoyancy force on the float when it is completely submerged? You might need a reminder that the volume of a sphere is V = 4/3π(r)3

• 2) Here's a slightly tougher one. If the float must have an upward buoyancy force of 3.0 N to shut off the ballcock valve, what percentage of the float will be submerged?

Buoyancy• When the weight of the submerged object…

– is greater than the buoyant force, the object will sink to the bottom

– is equal to the buoyant force, the object will remain at any level (like a fish)

– is less than the buoyant force, the object will rise to the surface and float

• In terms of density, if the object is – denser than the fluid, it will sink– the same density as the fluid, it will neither sink or

float– less dense than the fluid, it will float

Can a ship made of concrete float?

• Concrete is usually more dense than water, and will therefore normally sink when placed in water.

SS Selma, scuttled in Galveston Harbor, concrete tanker ship used during World War I

Apparent Weight = Fg-Fb

Apparent Weight• Apparent weight depends on the density• Apparent weight = Fg – Fb = ρoVog – ρfVfg• For a submerged object:

• A piece of metal weighs 50.0 N in air, 36.0 N in water, and 41.0 N in an unknown liquid. Find the densities of the following:

• The metal• The unknown liquid

f

o

f

o

B

g

Vg

Vg

F

objectF

)(

Problem…

• A cubic decimeter, 1.00 X 10-3 m3, of aluminum is submerged in water. The density of aluminum is 2.70 X 103kg/m3

– What is the magnitude of the buoyant force acting on the metal?

– What is the apparent weight of the metal?

Archimedes’ Principle• Palmer drops an ice cube into his glass of water. The ice,

whose density is 917 kg/m3, has dimensions 0.030 m x 0.020 m x 0.020 m. What is the buoyant force acting on the ice?

• William’s wedding ring, presumed to be pure gold, has a mass of 0.1 kg. When submerged in water its apparent mass is 0.080 kg. The density of water is 1000 kg/m3 which is equivalent to 1 kg/L.

• What is the buoyant force in Newtons?• What volume of water (in liters) is displaced?• Is the ring made of pure gold (ρ = 19.3 kg/L)?

• Pine is 0.50 as dense as water and therefore floats in water. Weight density of water is 9800 N/m3 or 9.80 N/L.

• What weight of water will be displaced by 25 kg of floating pine?• What additional force would be required to poke the pine beneath the

surface so it is completely submerged?

Hydrometers

• Simple devices used to determine the density (specific gravity) of a fluid.

What do you think????

• You are floating in a small raft in your pool. There's a brick in the raft. You toss the brick out of the raft and into the pool. The brick sinks to the bottom of the pool. Does the water level at the side of the pool rise, stay the same, or decrease?

Germany “Water Bridge”

Did this bridge have to be designed to withstand the additional weight of ship and barge traffic, or just the weight of the water?

Streamlines• Lines drawn to represent the flow of a fluid

• Velocity of fluid is tangent to the streamline

Streamlines

• Can be used to represent either Laminar or Turbulent flow.

Laminar and turbulent flow over a submarine

Transition from laminar to turbulent flow can be seen occurring down the length of this missile-body model captured by shadowgraph in high-speed flow.

Notice how the angle of attack of the wing can change the flow of air over the wing.As flow becomes turbulent, drag increases and lift is lost.This condition is known as “stall”

Turbulence in Mt. Spurr eruption, Alaska, 1992