1. Forces and Pressures in Fluids
8.5

2. Have you ever wondered why you feel lighter in water?

3. Or Noticed how easy it is to lift yourself up and out of a swimming pool?
It is much easier than doing it on land.
The reason why is because the water is exerting an upward force on you.

4. Or how a boat floats?
A boat has a special shape that is designed to push water aside. The more water that is pushed aside, the more force that the water exerts upward.

5. TO demonstrate
Let’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 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
The water has exerted a force of 1 N on this rock.
We call this force Buoyancy.
** I converted grams to N and rounded.**

6. 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 surface
Just to recap:
A force is a push or pull measured in Newtons.

7. 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
In the 3rd century BC, a greek mathematician

8. 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.
1 N
2 N

9. Archimedes’ Principle

10. Question for you...
Do all fluids exert the same buoyant force in an object?
No! If the fluid has a higher density then the object will still displace the same VOLUME of fluid BUT the mass of the fluid displaced will be more, therefore the weight will be more and the buoyant force will be more!

11. 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 N
We would need a buoyant force greater than 2 N.
1 N

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

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

14. 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:
Scuba divers use weights and a buoyancy control device (BCD) to help them maintain neutral buoyancy.
While a scuba diver is neutrally buoyant he or she can swim and move underwater without rising to the top or sinking.

15. Buoyancy equation B = (Vobject )( ρfluid)(gravity)
Buoyancy equals the volume of the object multiplied by the density of the fluid.
Note that gravity on Earth is 9.8 m/s2
greek letter rho

16. Let’s practice We need to know the volume and the density of the fluid
How would we calculate the buoyancy of a 7.62 cm long piece of 1” PVC piping.
What do we need to know to solve for buoyancy?
We need to know the volume and the density of the fluid

17. What is the volume of this piece of PVC?
15 mL
Remember to measure the water from the bottom of the meniscus.

18. Remember: the density of fresh water water is 1 g/cm3
Now, we take the volume of the PVC, 15mL, and multiply it with the density of the fluid.
Remember: the density of fresh water water is 1 g/cm3
and 1 mL = 1 cm3
B = (15mL)(1g/cm3)(9.8m/s2)
B = 147 N

19. 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

20. B = (Vobject )( ρfluid)(gravity) B = (15 ml) (1.03 g/cm3 ) (9.8m/s2)
B = N
This is why it is easier to float in salt water than fresh water.
If it was liquid mercury with a density of g/cm3 then the buoyant force would be N

21. 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.
The weight of the block is greater than the weight of the water it displaced so it will sink.

22. 10 cubic meters of displaced water has a weight of 98,000 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.
The steel boat will settle in the water until it reached a level where it displaced 76,000 N of water. At this point the upward force exerted by the water will equal the downward force by gravity.