1. Physics Chapter 8 Fluid Mechanics

2. Density
ρ = M V Therefore: ρV = M

3. Chapter 8
Density

4. Fig. T9.3, p. 262
Slide 13

5. Archimedes’s Principle
Any object completely or partially submerged in a fluid is buoyed up by a force whose magnitude is equal to the weight of the fluid displaced by the object.

6. Buoyant Force The upward force is called the buoyant force
The physical cause of the buoyant force is the pressure difference between the top and the bottom of the object

7. Buoyant Force, cont.
The magnitude of the buoyant force always equals the weight of the displaced fluid
The buoyant force is dependent on the volume of the object and the density of the fluid it is submerged in.
For a floating object, the buoyancy force must equal the weight of the object.
B=W
Some objects may float high or low

8. T = waterVg – alcoholVg T = (water – alcohol )Vg
Example: A balloon having a volume of 1.5 cubic meters is filled with ethyl alcohol and is tethered to the bottom of a swimming pool. Calculate the tension in the cord tethering it to the bottom of the swimming pool.
Fy = B – T – W = 0
Therefore, T = B – W
T = waterVg – alcoholVg
T = (water – alcohol )Vg
T = (1000kg/m3 – 806kg/m3) (1.5m3)(9.8m/s2)
T = N B
FBD T W

9. 11.6 Archimedes’ Principle
Example 9 A Swimming Raft
The raft is made of solid square
pinewood. Determine whether
the raft floats in water and if
so, how much of the raft is beneath
the surface.

10. 11.6 Archimedes’ Principle

11. 11.6 Archimedes’ Principle
The raft floats!

12. 11.6 Archimedes’ Principle
If the raft is floating:

13. Pressure
P = F N A m2 Pascal’s Principal 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.

14. Hydraulic Lift
P1 =P2
Therefore:
F1 = F2
A A2
F2, A2
F1, A1

15. Pressure at a Depth P = F = mg = ρVg = ρAhg = ρhg A A A A
Find the pressure on the bottom
of the submarine due to the water
above it.
And air above it.
330 m

16. Equation of Continuity
A1v1 = A2v2
The product of the cross-sectional area of a pipe and the fluid speed is a constant
Speed is high where the pipe is narrow and speed is low where the pipe has a large diameter
Av is called the flow rate

17. How Airplanes Wings Work