Forces and Pressures in Fluids

8.5

Have you ever wondered why you feel lighter in water?

Or Noticed how easy it is to lift yourself up and out of a swimming pool?

Or how a boat floats?

TO demonstrateLet’s say we tie a piece of string to a rock and measure its weight with a spring scale. The scale tells us that its weight is 2 N.

Next we put the rock in

water and don’t allow it to touch

the sides or the bottom.

Now the spring scale is

telling us that the

rock weighs

1 N.

2 N 1 N

Buoyancy is a measure of the upward force a fluid exerts on an object.

• It is easier to lift a boulder submerged on the bottom of a riverbed than to lift it above the water’s surfaceJust to recap:

A force is a push or pull measured in Newtons.

Archimedes

Realized that the force exerted on an object in a liquid is equal to the weight of the liquid displaced by the object.

Pushing water aside is called displacement of water

Archimedes’ Principle

States that the buoyant force on an object in a fluid is equal to the weight of the fluid displaced by the object.Archimedes’ principle tells us that the fluid displaced by this rock had a weight of 1N.

2 N

1 N

Archimedes’ Principle

Question for you...

Do all fluids exert the same buoyant force in an object?

Why objects sink or float

If the buoyant force is greater than the objects weight, the object will float.So in this example what do we need the buoyant force to be to make this rock float?

2 N1 N

Giant cargo ships may weight thousands of tons but they displace thousand of tons of water, which is why they do not sink.

Sink or Float

If the buoyant force is less than the object’s weight, then the object will sink.

Sink or float or Just stay put

When the weight is equal to the buoyant force, the submerged object will remain at any level, like a fish.

• This is called Neutral Buoyancy

• NASA video on neutral buoyancy training:• http://brainbites.nasa.gov/underwater/

Buoyancy equation

B = (Vobject )(  ρfluid)(gravity)

Buoyancy equals the volume of the object multiplied by the Buoyancy equals the volume of the object multiplied by the density of the fluid. density of the fluid.

Note that gravity on Earth is 9.8 m/sNote that gravity on Earth is 9.8 m/s22

Let’s practice

How would we calculate the buoyancy of a 7.62 cm long piece How would we calculate the buoyancy of a 7.62 cm long piece of 1of 1”” PVC piping. PVC piping.

What do we need to know to solve for buoyancy?What do we need to know to solve for buoyancy?

What is the volume of this piece of PVC?

Remember to measure Remember to measure the water from the the water from the bottom of the bottom of the meniscus. meniscus.

Now, we take the volume of the PVC, 15mL, and multiply it Now, we take the volume of the PVC, 15mL, and multiply it with the density of the fluid. with the density of the fluid.

• Remember: the density of fresh water water is 1 g/cmRemember: the density of fresh water water is 1 g/cm33

• and 1 mL = 1 cmand 1 mL = 1 cm33

•

B = (15mL)(1g/cmB = (15mL)(1g/cm33)(9.8m/s)(9.8m/s22))• B = 147 NB = 147 N

Let’s change the fluid

What if that PVC piece was in salt water instead of fresh water? What would the buoyant force be?

Reminder: The density of salt water is 1.03 g/cm3

B = (Vobject )(  ρfluid)(gravity)B = (15 ml) (1.03 g/cm3 ) (9.8m/s (9.8m/s22))B = 151.41 N

Why does a block of steel sink, but a steel boat floats?

A cubic meter of steel has a weight of 76,000 N. When placed in water, the block would displace one cubic meter of water.1 cubic meter of water weighs 9,800 N.

If the same block of steel is flattened into a thin sheet, its sides bent up into the shape of a boat, it may occupy 10 cubic meters of space instead of 1.10 cubic meters of displaced water has a weight of 98,000 N.The steel still weighs 76,400 N.Now the displaced water weighs more than the steel.