fluid dynamics
DESCRIPTION
Fluid Dynamics. Fluid Dynamics. Fluid dynamics is the study of how fluids (gases or liquids) flow. Because water is such a common fluid, fluid dynamics is often called hydrodynamics. Discharge. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/1.jpg)
![Page 2: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/2.jpg)
Fluid dynamics is the study of how fluids (gases or liquids) flow. Because water is such a common fluid, fluid dynamics is often called hydrodynamics.
![Page 3: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/3.jpg)
When fluid flows through a pipe, the flow or discharge (J) is the mass {J} (or volume {Q}) of fluid that passes a given point per unit of time.
![Page 4: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/4.jpg)
Mathematically:
Q = Av
![Page 5: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/5.jpg)
Describing discharge as mass per unit time is actually more correct, but if the pipe is full of an incompressible (constant ) fluid then either description is fine.
![Page 6: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/6.jpg)
i.e.
J =m/t = V/t = Al/t = Av
Since is usually constant, discharge in terms of volume is…
Q = Av
![Page 7: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/7.jpg)
If an incompressible fluid fills a pipe and flows through it, the discharge stays constant even if the diameter of the pipe changes.
![Page 8: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/8.jpg)
Mathematically:
Q = A1v1 = A2v2 = constant
![Page 9: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/9.jpg)
We can study fluid flow patterns with wind tunnels:
![Page 10: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/10.jpg)
There are many types.
![Page 11: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/11.jpg)
Some are wicked cool!
![Page 12: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/12.jpg)
Some contain wicked cool things!
![Page 13: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/13.jpg)
After designing models based on computed calculations of flow characteristics, the predictions can be checked with a flow test. http://www.esa.int/esaCP/ESA9DBG18ZC_index_0.html
![Page 14: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/14.jpg)
There are two main types of fluid flow:
and
![Page 15: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/15.jpg)
Laminar flow (AKA streamline flow) occurs when the particles of the fluid follow smooth, noncrossing paths.
![Page 16: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/16.jpg)
Note that during laminar flow, neighboring layers of the fluid slide by each other smoothly.
![Page 17: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/17.jpg)
Note that this is a shearing process.
![Page 18: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/18.jpg)
To study this process, two plates are separated by a thin layer of liquid.
![Page 19: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/19.jpg)
A force is applied to the top plate to make it move.
![Page 20: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/20.jpg)
The rapidity of the shearing motion is characterized by the shear rate of the two plates and the fluid between them.
![Page 21: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/21.jpg)
Shear rate = speed of top plate
distance between platesShear rate = v/L = s / t
![Page 22: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/22.jpg)
The viscosity of a fluid is the shear stress required to produce a unit shear rate.
![Page 23: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/23.jpg)
= viscosity = shear stress/shear rate.
= (F/A) / (v/L)
![Page 24: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/24.jpg)
= viscosity = shear stress/shear rate.
= (F/A) / (v/L) = (FL) / (vA)
FYI: = the lower Greek letter eta
![Page 25: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/25.jpg)
F vA / L for any given fluid. So the larger the value, the greater the force resisting the attempted shear under a given set of conditions. (i.e. The fluid is stickier.)
![Page 26: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/26.jpg)
For liquids, the viscosity results from attractive forces between the molecules. For gases, the viscosity results from collisions between the molecules.
![Page 27: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/27.jpg)
The SI unit for is N.s/m2, or Pa.s. This is called the poiseuille (Pl). Other units are the cgs unit the poise (P), for which 1 P = 0.1 Pl, and prefix versions of each.
![Page 28: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/28.jpg)
The greater the viscosity in a fluid, the greater the heat generated as it is sheared under a given set of conditions.
![Page 29: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/29.jpg)
Because of viscosity, it takes a pressure difference at the ends of a horizontal pipe to have laminar fluid flow through it at a steady rate. A French scientist named Poiseuille studied this in the 1800s and developed the formula that bears his name:
Q = (r
4(P1-P2)) / (8L)
![Page 30: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/30.jpg)
Q = (r
4(P1-P2)) / (8L)
All My Loving
Pi r fourth delta P
Over 8 eta L
Shows how fast V’s flowing…
That’s Q
![Page 31: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/31.jpg)
When fluid flows beyond a certain speed, the laminar flow breaks down into turbulent flow.
![Page 32: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/32.jpg)
Turbulent flow is characterized by small whirlpools called eddies, which consume an enormous amount of energy. This increases the drag on the object in the fluid flow far above the drag created by viscosity during streamline (laminar) flow. For liquids in a pipe, this translates to a need for a much higher (and less predictable) ____________ to maintain the flow.
![Page 33: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/33.jpg)
The Reynold’s Number (NR) is a dimensionless experimental number that gives an indication of the velocity at which turbulence will occur in a fluid.
![Page 34: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/34.jpg)
Mathematically:
NR = vD/
Fluid flow will usually be laminar if NR does not exceed about 2000 for fluid flowing through a pipe, or about 10 for obstacles.
![Page 35: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/35.jpg)
In the 1700s, a mathematician named Daniel Bernoulli studied the pressure associated with moving fluids and came to a startling conclusion:
http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Bernoulli_Daniel.html
![Page 36: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/36.jpg)
Bernoulli’s Principle basically states that… As a fluid’s velocity increases, its internal pressure decreases!
![Page 37: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/37.jpg)
Bernoulli’s Principle applies to a variety of phenomena.
![Page 38: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/38.jpg)
Mathematically:
P1 + ½ v12 + gh1 = P2 + ½ v2
2 + gh2
![Page 39: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/39.jpg)
Bernoulli’s Equation is really a restatement of the Law of Conservation of Energy: The total energy of a closed system remains constant. (This is true unless there is a ____________ change.)
P1 + ½ v12 + gh1 = P2 + ½ v2
2 + gh2
![Page 40: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/40.jpg)
Since work is done whenever a force is applied through a distance,
work is done whenever pressure forces a volume of fluid to move as well.
P1 + ½ v12 + gh1 = P2 + ½ v2
2 + gh2
Note: W = (F/A) x A x lA A
![Page 41: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/41.jpg)
Also, since work must be done to accelerate an object, faster moving objects have more kinetic energy.
By replacing the m in the equation with Al, we can see that
P1 + ½ v12 + gh1 = P2 + ½ v2
2 + gh2
W = KE = ½ mv2
W = KE = ½ Vv2
![Page 42: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/42.jpg)
Lastly, since work must be done to raise an object, potential energy may be exchanged for kinetic energy.
By replacing the m in the equation with Al, we can see that
P1 + ½ v12 + gh1 = P2 + ½ v2
2 + gh2
W = PE = KE = mgh
W = PE = KE = Vgh
![Page 43: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/43.jpg)
So all the terms in Bernoulli’s Equation are really energy terms associated with a given volume movement.
P1V + ½ Vv12 + Vgh1 = Constant
This becomes:
P1 + ½ v12 + gh1 = Constant / V
![Page 44: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/44.jpg)
Note that Bernoulli’s Equation ignores viscosity and compressibility. Reality is more closely modeled with the Navier-Stokes equation, but that is beyond the scope of this course.
![Page 45: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/45.jpg)
"That we have written an equation does not remove from the flow of fluids its charm or mystery or its surprise." --Richard Feynman [1964]
http://jef.raskincenter.org/published/coanda_effect.html
http://en.wikipedia.org/wiki/Richard_Feynman
![Page 46: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/46.jpg)
Long before Bernoulli entered the world, Torricelli realized that if a fluid were to flow from a w-i-d-e barrel, the fluid velocity would depend on the height of the fluid above the spigot. He determined that the formula was…
v =
![Page 47: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/47.jpg)
Long before Bernoulli entered the world, Torricelli realized that if a fluid were to flow from a w-i-d-e barrel, the fluid velocity would depend on the height of the fluid above the spigot. He determined that the formula was…
v = √2gh
![Page 48: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/48.jpg)
Why would that be? Well, if we modify Bernoulli we can derive this! (Note: essentially we are giving up _______, and gaining _______.)
P1 + ½ v12 + gh1 = P2 + ½ v2
2 + gh2
Since the air pressure doesn’t change much, P1 + ½ v1
2 + gh1 = P2 + ½ v22 + gh2
![Page 49: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/49.jpg)
Since the fluid is considered to be incompressible… P1 + ½ v1
2 + gh1 = P2 + ½ v22 + gh2
Since the top is still and the bottom is… the bottom… P1 + ½ v1
2 + gh1 = P2 + ½ v22 + gh2
![Page 50: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/50.jpg)
By rearrangement
v = √2gh
So Torricelli is an example of Bernoulli.
How about others?
![Page 51: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/51.jpg)
Bernoulli’s Principle explains the dynamic lift of flying birds and planes, venturi tubes (car carburetors, venturi meters, atomizers), air circulation in burrows, curveballs, many musical instruments, and TIAs.
![Page 52: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/52.jpg)
Bernoulli’s Principle helps to explain the dynamic lift that supports birds and airplanes.
![Page 53: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/53.jpg)
Note also that there are MANY ways to look at flight. Despite the differences in approach, they (the correct interpretations) all work.
http://hyperphysics.phy-astr.gsu.edu/hbase/fluids/airfoil.html#c1
![Page 54: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/54.jpg)
http://jef.raskincenter.org/published/coanda_effect.html
"In aerodynamics, theory is what makes the invisible plain. Trying to fly an airplane without theory is like getting into a fistfight with a poltergeist." --David Thornburg [1992].
![Page 55: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/55.jpg)
Dynamic lift occurs when a moving fluid is turned by a solid object.
http://www.av8n.com/irro/lecture_e.html
![Page 56: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/56.jpg)
Notice that the fluid travels faster over this wing, producing a net upward force, or lift.
http://www.av8n.com/irro/lecture_e.html
![Page 57: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/57.jpg)
Let’s study this a bit:
Link to: http://www.grc.nasa.gov/WWW/K-12/airplane/wrong2.html
![Page 58: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/58.jpg)
Question: Would this undercambered wing generate more or less lift than one which had a flat bottom?
Link to: http://www.grc.nasa.gov/WWW/K-12/airplane/wrong2.html
http://jef.raskincenter.org/published/coanda_effect.html
![Page 59: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/59.jpg)
1)The airfoil does NOT need to be curved.
2)Both the upper and lower surfaces affect the turning of the fluid.
Link to: http://www.grc.nasa.gov/WWW/K-12/airplane/wrong2.html
http://en.wikipedia.org/wiki/Airfoil
![Page 60: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/60.jpg)
The Coanda effect works like this… A fluid moving by a straight object moves straight.
![Page 61: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/61.jpg)
If an object is bent into the path of the fluid, the fluid bends to follow the object.
![Page 62: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/62.jpg)
But if an object is bent away from the path of the fluid, the fluid still bends to follow the object!
![Page 63: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/63.jpg)
The Coanda effect was named after the Romanian inventor Henri Coanda, who helped develop some of the first aircraft to utilize the jet engine.
http://en.wikipedia.org/wiki/Coand%C4%83_effect_movies
![Page 64: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/64.jpg)
http://hyperphysics.phy-astr.gsu.edu/hbase/fluids/kutta.html#c1
Curve balls curve because of Bernoulli.
![Page 65: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/65.jpg)
http://hyperphysics.phy-astr.gsu.edu/hbase/fluids/kutta.html#c1
Atomizers work because of Bernoulli.
![Page 66: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/66.jpg)
http://www.physics.lsa.umich.edu/demolab/demo.asp?id=27
Venturi tubes work because of Bernoulli.
![Page 67: Fluid Dynamics](https://reader035.vdocuments.net/reader035/viewer/2022062309/568159f0550346895dc7391f/html5/thumbnails/67.jpg)
Aspirators work because of Bernoulli.
http://hyperphysics.phy-astr.gsu.edu/hbase/fluids/aspirv.html#c1