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Lecture 11:

- Water distribution

- Air pressure

Reminders:

HW5 due Thursday 9pm

Reading for Thursday: 16.1 / 16.2 Tuesday

Midterm 2: 2 weeks from Thursday

I will put up estimated final grades sometime this week or

weekend so you have an idea where you stand

Water distribution is about Energy? Yes!

Bernoulli and Water distribution systems

Together this gives us several forms of

energy: 1. Heat (related to the temperature of an object but not the

same).

2. Gravitational Potential Energy (GPE) given by GPE = mgh

3. Work from another force (friction, hand, etc.) Work = F*d

(along direction)

4. Mechanical energy (energy stored in a spring) Not

quantitative

5. Kinetic energy (Energy of a moving object)

Still many other types.

6. Chemical (potential energy of bonds in materials)

7. Nuclear (potential energy in the nuclei of atoms)

8. Electrical energy (potential of a circuit or voltage to do

something)

9. Pressure Potential Energy TODAY!

Where does the water flow?

What determines the water pressure in different homes/heights?

How fast does water flow out of a faucet?

How do you pump water out of wells?

ALL ABOUT CONSERVATION OF ENERGY!

GPE = mgh KE = mv2 PPE = PV

Gravitational PE Kinetic Energy Pressure Potential

Pumps do work (Force x distance) (Energy from where)

Water distribution Or how conservation of energy governs EVERYTHING

reservoir pipe pump buildings

water tower

2. Bernoullis equation describes a. How the temperature of water changes as it flows through pipes.

b. The different amounts of water distributed to houses and industry

in a typical city.

c. The relationship between pressure, velocity, and height of water in

a pipe.

d. The relationship between the thickness of water pipes and the

pressure of the water they contain

1. Bernoullis equation is all about a. Conservation of momentum

b. Conservation of heat

c. Conservation of water

d. Conservation of potential energy

e. None of the above

3. When water leaves a hose through a nozzle, the pressure

a. Increases

b. Decreases

c. Stays the same.

Reading quiz

2. Bernoullis equation describes a. How the temperature of water changes as it flows through pipes.

b. The different amounts of water distributed to houses and industry

in a typical city.

c. The relationship between pressure, velocity, and height of water in

a pipe.

d. The relationship between the thickness of water pipes and the

pressure of the water they contain

1. Bernoullis equation is all about a. Conservation of momentum

b. Conservation of heat

c. Conservation of water

d. Conservation of potential energy

e. None of the above

3. When water leaves a hose through a nozzle, the pressure

a. Increases

b. Decreases

c. Stays the same.

Reading quiz

The super soaker (e.g. squirt guns)

Pump up the pressure inside just a little bit and squirt. If we pump it up

more, the water coming out will be:

a. going slower than before, b. going the same speed,

c. going faster.

(all of the physics of water distribution system)

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The super soaker (e.g. squirt guns)

Pump up the pressure inside just a little bit and squirt. If we pump it up

more, the water coming out will be:

a. going slower than before, b. going the same speed,

c. going faster.

You already know this from experience

Think conservation of energy. - Pumping does work, energy in arm stored (potential) energy in tank

- When press trigger, PPE KE of water

(all of the physics of water distribution system) Pressure potential energy (PPE)

What the heck is pressure anyway?

Pressure = Force

Area

The plunger of a syringe has an area of 1cm2.

I push the plunger with a force of 5N.

Whats the pressure exerted by the plunger on the fluid inside?

5N

a) 5N/m

b) 5 N/m2

c) 500N/m2

d) 50,000N/m

e) 50,000N/m2

Units: 1Pascal (Pa) = 1N/m2

Pressure potential energy (PPE)

What the heck is pressure anyway?

Pressure = Force

Area

Units: 1Pascal (Pa) = 1N/m2

The plunger of a syringe has an area of 1cm2.

I push the plunger with a force of 5N.

Whats the pressure exerted by the plunger on the fluid inside?

5N

a) 5N/m

b) 5 N/m2

c) 500N/m2

d) 50,000N/m

e) 50,000N/m2 Pressure = F/A = 5N/((0.01)(0.01))m2 = 50000 N/m2

= 50000 Pa

Blaise Pascal (1623-1662)

1 N/m2 is named 1 Pa (1 Pascal)

Child prodigy (started major contributions to mathematics at

16)

Influential mathematician, inventor, physicist, philosopher

invented some of the early modern calculators

Invented hydrostatics, hydrodynamics, the syringe

(multiplies pressure)

Pressure potential energy (PPE)

New form of potential energy for fluids

PE is the energy of an object (or fluid) due to its CONDITION (situation, surroundings etc)

Water of mass m, at height h has associated GPE = mgh because of its (vertical) position

- work (mgh) was done to get the water from ground to that height

What does this work for reservoirs?

- Physical details of how the work was done or how water is being

supported is not important

Water of volume V at pressure P has associated Pressure Potential Energy or PPE = PV

- Work (PV) was done to pressurize the water

- Physical details of how the work was done or how the pressure is

being maintained are not important

Check that PV has units of energy (J)

PV = N m3 = Nm = J

m2

Forms of energy in Super Soaker

Pressure

1. Pumping does work

transforming chemical

energy in my arm into

PPE.

Converts PPE into KE = mv2 2. When I pull the

trigger, pressure does

work on the water.

Pressure

I apply a force, compress pump by a distance. Work = force X distance.

What is

causing the

stream to

curve down?

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The same three forms of energy exist in a water distribution system If we add up energy in these forms, the sum must be constant. It just sloshes back and forth between forms!

notice we dropped the 1 atmosphere inside and out.

PV + mv2 + mgh = Etotal

Energy in a water distribution system

Since Etotal is constant:

If one form of E changes, the other quantities must change correspondingly. - If pressure changes (water comes out of nozzle), v changes.

- If height changes (go up in building), pressure or v changes, etc.

Like the cart coasting up and down hills with no friction. Velocity and height are always connected

If you know velocity and height at one place, can calculate it at all others.

PPE + KE + GPE = Etotal (constant)

notice we dropped the 1 atmosphere inside and out.

Bernoullis Equation PV + mv2 + mgh = Etotal

But what mass of water are we talking about, what height?

Consider one little bit of water of volume V and mass m:

Replace m = rV where r is the fluid density (r = mass/volume

= 1000kg/m3 for water)

PV + rVv2 + rVgh = Etotal

We can divide through by V to get the standard form for Bernoullis equation:

P + rv2 + rgh = Etotal/V (Etotal per unit volume )

Just good old conservation of energy with the terms relabeled

Since Etotal per vol is constant:

Know P, v and h at one point can calculate these quantities at another

How is velocity of water out related to pressure inside gun?

Pinside

P + r v2 = Etotal per vol (constant)

Inside gun: P = Atmos Pres. + Ppump v= 0 AP + Ppump = Etotal per vol

Outside gun: P =Atmos Pres., voutside is big AP + r voutside2 = Etotal per vol

Apply Bernoulli to Squirt Gun

P + rv2 + rgh = Etotal per vol Height constant so ignore GPE

voutside

AP + Ppump = AP + r voutside2

Ppump = r voutside2

voutside = sqrt(2 Ppump / r)

Faucet shut off, so

water is not moving.

Bernoullis Equation:

P + rv2 + rgh = Etpv

Compare water at surface and at depth H

v = 0 everywhere P + rgh = Etpv

At surface: P = AP, h = 0

Etpv = AP

At depth H: P = AP + Pw, height = -H

Etpv = AP + Pw + rg(-H)

Etpv constant AP = AP + Pw rgH

0 = Pw rgH

Pw = rgH PH = AP + rgH

More on pressure

Heres a bucket of water with a faucet attached. What is the pressure at a depth H?

H

P?

h = 0

Faucet shut off, so

water is not moving.

Bernoullis Equation:

P + rv2 + rgh = Etpv

Compare water at surface and at depth H

v = 0 everywhere P + rgh = Etpv

At surface: P = AP, h = 0

Etpv = AP

At depth H: P = AP + Pw, height = -H

Etpv = AP + Pw + rg(-H)

Etpv constant AP = AP + Pw rgH

Pw = rgH PH = AP + rgH

More on pressure

Heres a bucket of water with a faucet attached. What is the pressure at a depth H?

H

This pressure is exerted equally in all directions

AP + rgH

Atmospheric pressure

Faucet shut off, so

water is not moving.

Pressure at surface of water

= Atmospheric pressure (AP)

100,000 Pa (about 84 kPa in Boulder)

Pressure due to air molecules hitting surface and exerting a force

Always present at surface of earth

Usually only interested in CHANGES in water pressure and AP cancels out

If so can set zero of water pressure at AP (like setting zero of height somewhere

convenient)

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With the faucet off, the water is stopped at point C.

Rank the pressures at the three locations shown.

A

B C

a) PA < PB < PC b) PA < PB = PC c) PA = PB = PC d) PA = PB > PC

With the faucet off, the water is stopped at point C.

Rank the pressures at the three locations shown.

A

B C

a) PA < PB < PC b) PA < PB = PC c) PA = PB = PC d) PA = PB > PC

A: AP

B: AP + rgH

C: same pressure as B because they

are at the same depth.

H