CHAPTER 6 – Fluids in Motion

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CHAPTER 6 – Fluids in Motion Garden Watering Balls and Air Airplanes New Physics: viscosity, boundary layer, turbulence, chaos lift, drag, pressure drag, Magnus force, wake airfoil, streamlining, (propeller) thrust, jet engine VORTEX CANNON Garden Watering Introductory Question

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CHAPTER 6 – Fluids in Motion
• Garden Watering
• Balls and Air
• Airplanes
• New Physics:
• viscosity, boundary layer, turbulence, chaos
• lift, drag, pressure drag, Magnus force, wake
• airfoil, streamlining, (propeller) thrust, jet engine

### Garden WateringIntroductory Question

Water pours weakly from an open hose but sprays hard when you cover most of the end with your thumb. When is more water coming out of the hose?

A. When the hose end is uncovered

B. When your thumb covers most of the end

Faucets allow you to control water flow

Faucets make noise when open

Longer, thinner hoses deliver less water

Water sprays faster from a nozzle

Water only sprays so high

A jet of water can push things over

• How much does the diameter of a hose matter?
• Why does water pour gently from an open hose?
• Why does water spray so hard from a nozzle?
• How does a faucet control flow?
• What causes hissing in a faucet, hose, or nozzle?
• Why do pipes rattle when you close the faucet?
Water velocity profile in a pipe
• Boundary layer: zero velocity!
• dust on a fan blade
• washing a car with a water hose
Viscous Forces and Viscosity
• Viscous forces
• oppose relative motion within a fluid
• and are similar to sliding friction: they waste energy
• Fluids are characterized by their viscosities
• measure of the strength of the viscous forces
• caused by chemical interactions within the fluids

Honey, very viscous: laminar flow

(Coloured) water, less viscous: turbulent flow

Approximate Viscosities of a Variety of Fluids

TABLE6.1.1

1 Pa·s = 1kg/m·s

No viscosity  superfluid (component of ultracold liquid He)

Motor oil, 10W40

Superfluidity

Superfluid He will "creep" along surfaces in order to find its own level - after a short while, the levels in the two containers will equalize. The Rollin film also covers the interior of the larger container; if it were not sealed, the helium II would creep out and escape.

Question 1
• How much does the diameter of a hose matter?
• Is a 5/8” hose much different from a 3/4” hose?
Hoses and Water Flow (part 1)
• The rate at which water flows through a hose,
• increases as end-to-end pressure difference increases
• decreases as water’s viscosity increases,
• decreases as hose becomes longer,
• and increases dramatically as hose becomes wider
• Increasing the hose width
• enlarges cross-sectional area through which to flow
• and lets water get farther from the walls of the hose
Hoses and Water Flow (part 2)
• Water flow through a hose is proportional to
• pressure difference
• 1/viscosity
• 1/hose length
• (pipe diameter)4
• Poiseuille’s Law:
Question 2

Why does water pour gently from an open hose?

Wasting Energy in a Hose
• Viscous effects
• waste water’s total energy as thermal energy
• and become stronger with increased flow speed
• Faster flow leads to more viscous energy loss
• faster flow  more relative motion of laminas
• Faster flow causes quicker loss of pressure
Question 2

Why does water pour gently from an open hose?

An open hose allows the water to flow quickly through it. This means large viscous forces will do negative work, transforming pressure PE into thermal energy. The pressure difference at the hose end will be small, so the resulting water KE will be, too.

Introductory Question (revisited)

Water pours weakly from an open hose but sprays hard when you cover most of the end with your thumb. When is more water coming out of the hose?

When the hose end is uncovered

When your thumb covers most of the end

• Blockage  water travels slowly through the hose, encountering smaller viscous forces. It therefore loses little energy, and so its pressure is large at the hose end. The large pressure difference then accelerates it to high speed when it exits the hose.
Introductory Question (re-revisited)

Water pours weakly from an open hose but sprays hard when you cover most of the end with your thumb. When is more water coming out of the hose?

When the hose end is uncovered

When your thumb covers most of the end

Making Water Accelerate
• Even in steady-state, water can accelerate
• but in cylindrical pipes, forward acceleration would leave gaps and backward acceleration would cause jams
• so acceleration must involve turning
• Acceleration toward the side (turning)
• requires obstacles
• and involves pressure imbalances
• and changes in speed
Bending the Flow in a Hose

Streamlines 

Turning is accelerating

Since water accelerates toward lower pressure,

water flow needs a

pressure imbalance

to bend

Streamlines
• Point in the direction of the local water velocity
• Their density varies directly with the local water speed, and so inversely with pressure (by Bernoulli’s equation)

The flow naturally develops a pressure gradient

• higher pressure & lower speed on the outside of the bend
• lower pressure & higher speed on the inside of the bend
• and water accelerates fromhigh pressure to lower pressure
Question 3

Why does water spray so hard from a nozzle?

Speeding the Flow in a Nozzle

Since water must speed up through a nozzle,

it needs a pressure imbalance to push it forward

The flow naturally develops a pressure gradient

• lower pressure & higher speed as the neck narrows: pressure PE  KE
Question 4
• How does a faucet control flow?
• Why is a small opening different from a large one?
Faucets and Water Flow
• In going through a faucet, water must
• flow through a narrow passage
• and pass close to the faucet’s stationary surfaces
• Total energy limits flow speed through passage
• The water turns its total energy into kinetic energy,
• but its peak speed is limited by its initial pressure
• Motion near the surfaces slows the water
• Because water at the walls is stationary,
• viscous forces within the water slow all of it
Question 5

What causes hissing in a faucet, hose, or nozzle?

Roaring rapids?

Stethoscope diagnoses heart problem?

Water Flow Isn’t Always Smooth
• We’ve been examining laminar flow
• in which viscosity dominates the flow’s behavior
• and nearby regions of water remain nearby
• a lamina is a thin sheet
Turbulent Flow
• Inertia dominates the flow’s behavior
• and nearby regions of water become separated
• An example of chaos: extreme sensitivity to initial conditions
• But when is flow laminar and when is it
• non-laminar=turbulent?
Reynolds Number

The flow type depends on the Reynolds number

Below ~2300 viscosity wins, so flow is laminar

Above ~2300 inertia wins, so flow is turbulent

Common feature of turbulent flow: THE VORTEX

The object creates a wake of shed vortices in the flow above.

Question 6

Why do pipes rattle when you close the faucet?

“water hammer”

Water and Momentum
• Water carries momentum
• Water transfers its momentum via impulses:

impulse = pressure· surface area· time

• Large momentum transfers requires
• large pressures,
• large surface areas,
• and/or long times.
• Moving water can be surprisingly hard to stop
Summary: Garden Watering

Total energy limits speed, height, and pressure

Bending water flows develop pressure gradients

Nozzles exchange pressure for speed

Viscosity wastes flowing water’s total energy

Turbulence wastes flowing water’s total energy

Wasted total energy because thermal energy

Moving water has momentum, too