Download - Class 11
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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