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Making connections: take-home investigation with two strips of paper

For a good illustration of Bernoulli’s principle, make two strips of paper, each about 15 cm long and 4 cm wide. Hold the small end of one strip up to your lips and let it drape over your finger. Blow across the paper. What happens? Now hold two strips of paper up to your lips, separated by your fingers. Blow between the strips. What happens?

Velocity measurement

[link] shows two devices that measure fluid velocity based on Bernoulli’s principle. The manometer in [link] (a) is connected to two tubes that are small enough not to appreciably disturb the flow. The tube facing the oncoming fluid creates a dead spot having zero velocity ( v 1 = 0 size 12{v rSub { size 8{1} } =0} {} ) in front of it, while fluid passing the other tube has velocity v 2 size 12{v rSub { size 8{2} } } {} . This means that Bernoulli’s principle as stated in P 1 + 1 2 ρv 1 2 = P 2 + 1 2 ρv 2 2 size 12{P rSub { size 8{1} } + { {1} over {2} } ρv rSub { size 8{1} } "" lSup { size 8{2} } =P rSub { size 8{2} } + { {1} over {2} } ρv rSub { size 8{2} } "" lSup { size 8{2} } } {} becomes

P 1 = P 2 + 1 2 ρv 2 2 . size 12{P rSub { size 8{1} } =P rSub { size 8{2} } + { {1} over {2} } ρv rSub { size 8{2} } "" lSup { size 8{2} } "." } {}
Part a of the figure shows a picture of a wing. It is in the form of an aerofoil. One side of the wing is broader and the other end tapers. The direction of the air is shown as lines along the length of the wing. The direction of the air below the wing is shown as flowing along the length of the wing. The pressure exerted by the air given by P b is upward. The direction of the air on the top or front part of the wing is shown as flowing along the length of the wing. The pressure exerted by the air is given by P f, and it acts downward. Part b of the figure shows a boat with a sail. The direction of the sail is almost across the boat. The direction of the air in the sail is shown by lines on the front and back sides of the sail. The air currents on the front exert a pressure P front toward the sail, and air currents on the back sides of sail exert a pressure P back again toward the sail.
(a) The Bernoulli principle helps explain lift generated by a wing. (b) Sails use the same technique to generate part of their thrust.

Thus pressure P 2 size 12{P rSub { size 8{2} } } {} over the second opening is reduced by 1 2 ρv 2 2 size 12{ { { size 8{1} } over { size 8{2} } } ρv rSub { size 8{2} } rSup { size 8{2} } } {} , and so the fluid in the manometer rises by h on the side connected to the second opening, where

h 1 2 ρv 2 2 . size 12{h prop { {1} over {2} } ρv rSub { size 8{2} } rSup { size 8{2} } "."} {}

(Recall that the symbol size 12{ prop } {} means “proportional to.”) Solving for v 2 size 12{v rSub { size 8{2} } } {} , we see that

v 2 h . size 12{v rSub { size 8{2} } prop sqrt {h} "."} {}

[link] (b) shows a version of this device that is in common use for measuring various fluid velocities; such devices are frequently used as air speed indicators in aircraft.

Part a shows a U-shaped manometer tube connected to ends of two tubes which are placed close together. Tube one is open on the end and shows a velocity v one equals zero at the end. Tube two has an opening on the side and shows a velocity v two across the opening. The level of fluid in the U-shaped tube is more on the right side than on the left. The difference in height is shown by h. Part b of the figure shows a velocity measuring device a pitot tube. Two coaxial tubes, one broader outside and other narrow inside are connected to a U-shaped tube. The U-shaped tube is also narrow at one end and broader at the other. The narrow end of the U-shaped tube is connected to the narrow inner tube and the broader end of the U-shaped tube is connected to the broader outer tube. The tube one has an opening at one of its edges and the velocity of the fluid at the end is v one equals zero. Tube two has an opening on the side and shows a velocity v two across the opening. The level of fluid in the U-shaped tube is more on the right side than on the left. The difference in height is shown by h.
Measurement of fluid speed based on Bernoulli’s principle. (a) A manometer is connected to two tubes that are close together and small enough not to disturb the flow. Tube 1 is open at the end facing the flow. A dead spot having zero speed is created there. Tube 2 has an opening on the side, and so the fluid has a speed v across the opening; thus, pressure there drops. The difference in pressure at the manometer is 1 2 ρv 2 2 size 12{ { { size 8{1} } over { size 8{2} } } ρv rSub { size 8{2} } rSup { size 8{2} } } {} , and so h is proportional to 1 2 ρv 2 2 size 12{ { { size 8{1} } over { size 8{2} } } ρv rSub { size 8{2} } rSup { size 8{2} } } {} . (b) This type of velocity measuring device is a Prandtl tube, also known as a pitot tube.

Summary

  • Bernoulli’s equation states that the sum on each side of the following equation is constant, or the same at any two points in an incompressible frictionless fluid:
    P 1 + 1 2 ρv 1 2 + ρ gh 1 = P 2 + 1 2 ρv 2 2 + ρ gh 2 . size 12{P rSub { size 8{1} } + { { size 8{1} } over { size 8{2} } } ρv rSub { size 8{1} } rSup { size 8{2} } +ρ ital "gh" rSub { size 8{1} } =P rSub { size 8{2} } + { { size 8{1} } over { size 8{2} } } ρv rSub { size 8{2} } rSup { size 8{2} } +ρ ital "gh" rSub { size 8{2} } } {}
  • Bernoulli’s principle is Bernoulli’s equation applied to situations in which depth is constant. The terms involving depth (or height h ) subtract out, yielding
    P 1 + 1 2 ρv 1 2 = P 2 + 1 2 ρv 2 2 . size 12{P rSub { size 8{1} } + { { size 8{1} } over { size 8{2} } } ρv rSub { size 8{1} } rSup { size 8{2} } =P rSub { size 8{2} } + { { size 8{1} } over { size 8{2} } } ρv rSub { size 8{2} } rSup { size 8{2} } } {}
  • Bernoulli’s principle has many applications, including entrainment, wings and sails, and velocity measurement.

Conceptual questions

You can squirt water a considerably greater distance by placing your thumb over the end of a garden hose and then releasing, than by leaving it completely uncovered. Explain how this works.

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Water is shot nearly vertically upward in a decorative fountain and the stream is observed to broaden as it rises. Conversely, a stream of water falling straight down from a faucet narrows. Explain why, and discuss whether surface tension enhances or reduces the effect in each case.

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Look back to [link] . Answer the following two questions. Why is P o size 12{P rSub { size 8{o} } } {} less than atmospheric? Why is P o size 12{P rSub { size 8{o} } } {} greater than P i size 12{P rSub { size 8{i} } } {} ?

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Questions & Answers

it is a process in which electrolyte breaks down into its ions....
ABHISHEK Reply
ionization
Shang
A ball is thrown vertically upwards so that its max height is 100m...at the same instant another ball is dropped frm 100m above the ground...where will the two balls meet and why?
Blessing Reply
50m
wenhe
why?
Blessing
plz calculate the answer...
Blessing
😟
Blessing
75m
S.M
how?😨
Blessing
because they approach each other at different speeds, but same acceleration, so you can calculate its height above ground.
S.M
Yeah. He's right. Your question seems very similar to a question I did in physics class, and our answer was 50.so yeah that's why I said that. But 75m is correct
wenhe
what's is waves
nuraddeen
Waves is the disturbance of a medium such that the particles in the medium vibrate to cause the movement of energy from one point to another without the the particle itself moving.
Prince
what is the medium that light waves travel through?
Luke
and electrons, protons, neutrons and quarks for that matter?
Luke
it's spacetime that light and every other particles travel through actually
S.M
ether
Anand
for above question, i think 50m is the correct answer. the first ball will behave exactly like 2nd ball when it reaches 100m (max height).
James
From rest, a body moves with an acceleration of 8m/s in 10 secs. calculate the distance during the 8th seconds
Caleb
please use energy conservation to solve this problem. i think i have an answer but it is too long to explain here.
James
one is with some initial velocity v, while other one will start it's journey from rest, so they can't travel equal distance in equal amount of time
S.M
to be honest I knew the answer was just pointing out a flaw in above answer and light does not require a medium to travel through, this was proved in the 1887 by Michelson and Morley.
Luke
the two balls have different acceleration. the accelerations are same in magnitude but in different directions for them. so the first ball will gradually move slower and the 2nd ball will move faster.
James
u can just put 50m or 75m in equation to check whether right or not
James
the total energy of the two balls are equal, KE + PE. 1/2mv(1)^ 2 + mgh(1) = 1/2mv(2)^2 +mgh(2). use that
James
what's is electrolysis
nuraddeen
Give an example (but not one from the text) of a device used to measure time and identify what change in that device indicates a change in time.
David Reply
hour glass, pendulum clock, atomic clock?
S.M
tnks
David
A heart pumping blood would indicate a change in time as its volume or pressure changed. The ratio of displacement or change in configuration between any 2 systems can indicate time.
Khashon
how did they solve for "t" after getting 67.6=.5(Voy + 0)t
Martin Reply
Find the following for path D in [link] : (a) The distance traveled. (b) The magnitude of the displacement from start to finish. (c) The displacement from start to finish.
David Reply
the topic is kinematics
David
can i get notes of solid state physics
Lohitha
just check the chpt. 13 kinetic theory of matter it's there
David
is acceleration a fundamental unit.
David Reply
no it is derived
Abdul
no
Nisha
K thanks
David
no it's not its derived
Emmanuel
hi
Gift
Hello
Gift
hello gift
Emmanuel
hello
David
Hello Emmanuel
Gift
how are you gift
Emmanuel
I'm good
Gift
that's good
Emmanuel
how are you too
Gift
am cool
Emmanuel
spending time summarizing
Emmanuel
broadening my horizon
Emmanuel
I am fin
Longwar
ok
Gift
hi guys can you teach me how to solve a logarithm?
Villaflor Reply
how about a conceptual framework can you simplify for me? needed please
Villaflor
Hello what happens when electrone stops its rotation around its nucleus if it possible how
Afzal
I think they are constantly moving
Villaflor
yep what is problem you are stuck into context?
S.M
not possible to fix electron position in space,
S.M
Physics
Beatriz
yes of course Villa flor
David
equations of kinematics for constant acceleration
Sagcurse Reply
A bottle full of water weighs 45g when full of mercury,it weighs 360g.if the empty bottle weighs 20g.calculate the relative density of mercury and the density of mercury....pls I need help
Lila Reply
well You know the density of water is 1000kg/m^3.And formula for density is density=mass/volume Then we must calculate volume of bottle and mass of mercury: Volume of bottle is (45-20)/1000000=1/40000 mass of mercury is:(360-20)/1000 kg density of mercury:(340/1000):1/50000=(340•40000):1000=13600
Sobirjon
the latter is true
Sobirjon
100g of water is mixed with 60g of a liquid of relative density 1.2.assuming no changes in volume occurred,find the average relative density of the mixture...take density of water as 1g/cm3 and density of liquid 1.2g/cm3
Lila
plz hu can explain Heisenberg's uncertainty principle
Emmanuel Reply
who can help me with my problem about acceleration?
Vann Reply
ok
Nicholas
how to solve this... a car is heading north then smoothly made a westward turn during the travel the speed of the car remains constant at 1.5km/h what is the acceleration of the car? the total travel time of the car as it smoothly changed its direction is 15 minutes
Vann
i think the acceleration is 0 since the car does not change its speed unless there are other conditions
Ben
yes I have to agree, the key phrase is, "the speed of the car remains constant...," all other information is not needed to conclude that acceleration remains at 0 during the entire time
Luis
who can help me with a relative density question
Lila
1cm3 sample of tin lead alloy has mass 8.5g.the relative density of tin is 7.3 and that of lead is 11.3.calculate the percentage by weight of tin in the alloy. assuming that there is no change of volume when the metals formed the alloy
Lila
So it looks like you need a formula for rotational acceleration. Are you asking about its angular acceleration?
Khashon
morning, what will happen to the volume of an ice block when heat is added from -200°c to 0°c... Will it volume increase or decrease?
adefenwa Reply
no
Emmanuel
hi what is physical education?
Kate
BPED..is my course.
Kate
No
Emmanuel
I think it is neither decreases nor increases ,it remains in the same volume because of its crystal structure
Sobirjon
100g of water is mixed with 60g of a liquid of relative density 1.2.assuming no changes in volume occurred,find the average relative density of the mixture. take density of water as 1g/cm3 and density of liquid as 1.2g/cm3
Lila
Sorry what does it means"no changes in volume occured"?
Sobirjon
volume can be the amount of space occupied by an object. But when an object does not change in shape it will still occupy the same space. Thats why the volume will still remain the same
Ben
Most soilds expand when heated but if it changes state at 0C it will have less volume. Ice floats because it is less dense ie a larger mass per unit volume.
Richard
how to calculate velocity
Okwethu Reply
v=d/t
Emeka
his about the speed?
Villaflor
how about speed
Villaflor
v=d/t
Nisha
hello bro hw is life with you
Jacob Reply
Mine is good. How about you?
Chase
Hi room of engineers
lawan Reply
yes,hi sir
Okwethu
hello
akinmeji
Hello
Mishael
hello
Jerry
hi
Sakhi
hi
H.C
so, what is going on here
akinmeji
u are all wlc just ask your question anybody. can answer
Ajayi
good morning ppl
ABDUL
Practice Key Terms 2

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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