1. Fluids: Bernoulli’s Principle
PHYS16 – Lecture 33
On a windy day in 1735, a new wig gives Bernoulli an idea.
Fluids: Bernoulli’s Principle

2. Fluids pre-question
You are watering some flowers with a garden hose. You want to water some flowers in the very back of the garden. Assume that the flowers you want to water are at the same level as the hose. What do you have to do to the opening of the hose to increase the range by 4?
A) Decrease the area by a factor of 16
B) Decrease the area by a factor of 4
C) Decrease the area by a factor of 2
D) Increase the area by a factor of 2
E) Increase the area by a factor of 4

3. Outline for Fluids Fluid Statics Fluid Dynamics
Pressure and Pascal’s Principle
Buoyant Force and Archimedes’ Principle
Fluid Dynamics
Ideal Fluids
Equation of Continuity
Bernoulli’s Equation

4. Buoyant Force and anchors…
If I have a boat in a pond and I toss out an anchor what happens to the water level in the pond?

5. Fluid Dynamics: Ideal Fluids

6. Ideal Fluids Incompressible – density is a constant
Nonviscous – ignore frictional effects
Irrotational – doesn’t rotate
Laminar – no acceleration
Streamlines represent fluid flow

7. Ideal Fluids Mass is conserved Energy is conserved
Momentum is conserved
Continuum hypothesis is true – properties defined at infinitesimal points (density, pressure, temperature, etc.)

8. Which fluids are ideal? Water Air Honey Blood
Water – can be turbulent (waterfall not ideal, ideal in a slow moving river)
Air – compressible (piston not ideal, ideal in a laminar wind)
Honey – viscous fluid such that drag forces can’t be neglected (Not usually ideal)
Blood – pulsatile flow, filled with proteins/cells (ideal in large arteries or veins, not capillaries)

9. What happens if fluid is not ideal?

10. Poiseuille's Law When frictional forces dominate velocity decreases
Viscous fluids
Small Diameters
Ideal – larger diameters
With Friction – small diameters

11. Fluid Dynamics: Equation of Continuity

12. Equation of Continuity
For an ideal fluid flowing in a pipe, the volume flow rate through the pipe is constant
Narrower section
Larger speed
Wider section
Smaller speed

13. Example: Water out of faucet
Why does the stream of water flowing from a faucet often get more narrow as the water falls?
Gravity accelerates water so velocity increases. If velocity goes up, then area goes down…

14. Example: Arterial branching
An artery branches into two smaller arteries, each with half the diameter of the first. What is the velocity in the smaller artery compared to the larger artery?
Half
Same
Twice
Four times

15. Fluid Dynamics: Bernoulli’s Equation

16. Bernoulli’s Equation
For an ideal fluid flowing in a pipe, pressure in the pipe is related to the velocity and height of fluid

17. Discussion: Two sheets in the wind?
What happens if I take two sheets of paper, separate them by 1” and blow between them?
A) sheets will move apart
B) sheets will come together
C) sheets will stay at same spots

18. Main Points Buoyant force
Ideal fluid is incompressible, laminar, nonviscous, and irrotational
Equation of continuity
Bernoulli’s Equation