I. INTRODUCTION:
If some families were to be stranded on a desolate Pacific isle and wanted to survive and foster the beginnings of a civilization, the best hope would be if they had with them the works of Sir Isaac Newton (the laws of motion, c1687), the works of Faraday (electricity flows from a moving magnetic field, c1821) and the works of Bernoulli (how everything works, c1738)
If we had to choose one – it would be Bernoulli. Bernoulli explains why the front door closes to a Summer breeze, and how the carburetor works on a 55 Chevy. It explains how to design a sailboat to sail into the wind. It explains airfoils, and the propeller on your favorite outboard (and the one used on a Cessna). It explains the vapors seen streaming from the wingtips. It explains the aspirator used by asthma patients; and when the Wright brothers made the first flight from Kitty Hawk, North Carolina, c1903, Orville and Wilbur manned the tiller, while Bernoulli gave the wings lift and the propeller thrust to take the craft 120 feet down field (note 1, 4 and 5).
Bernoulli also explains buoyancy, and in effect, provides the mathematics for Archimedes principle, c200’s B.C., (note 2).
And if we were needing to make a waste water purification pond to service this isle civilization, we would enlist Bernoulli to manage the flow between aeration ponds.
But before we go on, we should correct two errors in the title. Bernoulli is not a theory – it is cold hard fact. Neither was it expressed as a theory or hypothesis. Bernoulli’s principle was written in the form of an energy equation with essentially four terms: (pressure) + (velocity) + (height potential) + (frictional and turbulence losses)
II. THE EFFECT OF PRESSURE IN BERNOULLI’S PRINCIPLE
Without a doubt – pressure is central to all functional devices that employ Bernoulli’s principle (see following discussion).
III. BERNOULLI’S PRINCIPLE:
Bernoulli’s principle was stated in equation form as follows:
The energy at any point within an open or closed flowing system = (the contributions from pressure) + (the contributions from velocity) + (potential contributions from height) + (loses from friction and turbulence)
The equation can be written in any manner of styles, but the following style is perhaps more intuitive (note 3). The units are in feet.
1.) e (energy at any point) = (p/gamma) + (v2/2g) + h + f
where: p = pressure, gamma (the Greek letter) = density of the fluid (pounds/cubic foot); v = average velocity; g = gravity; h = height potential, f = frictional losses measured between two locations in the flow path.
Equation 1. can be rewritten in a more useful and communicative format, as follows:
2.) e (energy at any point) = (p + v + h + f)
(NOTE: since equations 1 and 2 take into account all elements within the system, the equations can also be written: the total (p + v + h + f) is constant throughout the system
IV. BERNOULLI’S PRINCIPLE IN PRACTICE:
The main concept of Bernoulli’s principle may be stated in this fashion: (within a system) the pressure and velocity of flow are related in such a way that as the velocity increases, the pressure (at that same point) correspondingly decreases. The inverse is also true: when the velocity decreases, the pressure (at that same point) correspondingly increases.
But the principle is applied so broadly that it’s best understood by looking at the equation in several of its applications.
(NOTE: the equations use Absolute pressure not gauge pressure, see note 6)
A.) If we were designing or analyzing an open or closed fluid system (flowing water or hydraulics where height was a factor), we’d use all four terms from equation 2 above, and we’d compare energy along the system between points (“A” and “B”).
3.) e (across the system) = (p + v + h) at A (minus) (p + v + h + f) at B
NOTE: The friction term at A is not present because the friction is measured as a loss between A and B, hence it starts as zero at A
B.) If we were designing an air foil, or a sail or propeller, we’d not require the height potential, though it would be taken into affect in the density of a compressible fluid.
So the equation would be
4.) e (across the system) = (p + v + f) at A (minus) (p + v + f) at B
C.) If we were designing or analyzing a carburetor venturi, or an aspirator (we’d ignore height and friction) and use the following equation
5.) e (across the system) = (p + v) at A (minus) (p + v) at B
D.) If we wondered why a door closed to a summer breeze, we’d apply the main concept of Bernoulli’s equation (as velocity goes up, pressure goes down). From this we’d conclude (because the velocity of the summer breeze across an open door lowers the pressure) that the higher inside pressure would close the door against the aerodynamics of the wind.
E.) If we were to consider a situation where the velocity was so high that there was no pressure (or negative pressure) it would result in cavitation. Cavitation develops within a fluid when very high velocities cause a vacuum to form. The vacuum (i.e., negative pressure) is then encapsulated into tiny droplets by surface tension.
Real problems develop when the cavitation bubbles (examples of which are seen streaming from propellers, wing tips, or developing inside pumps, et cetera) implode. Implosion pressures can get well over 100’s of thousands of psi; this in turn erodes the paint and chips metal from propellers, and eats holes in inlet side pump plumbing. The implosion of cavitation bubbles is also the principle cause for the erosion of bridge foundations that are built in river waters.
V. CONCLUSION
It can be seen from the discussion and equations above that pressure is central to all functional devices that employ Bernoulli’s principle. Everything listed, and a dozen others, would not work without pressure.
VI. SOURCE OF THE PRESSURE
a.) All atmospheric related devices (airplanes, sails, helicopter blades, carburetors, aspirators, et cetera) work solely on atmospheric pressure: 14.7 psi at sea level.
b.) Pump inlets (unless super charged, or have a hydraulic head) also work solely on atmospheric pressure, while down stream pressure is developed as a function of the pump and the down steam resistance of the system.
VII. EPILOGUE
One of the most graceful birds ever, is the Swallow-tailed Kite. It is black and white and has a long forked tail. There are several that live close. One day one of them lost a tail feather and it fell into the yard. Later, as the feather lay on a table, a slight breeze passed over and lifted it straight up into the air. From this we can surmise that birds can hover, at least in part, because their feathers have aerodynamic lift. Aerodynamic lift means that there is a velocity induced differential pressure between the upper and lower surfaces of the feather.
Might this same occurrence have been witnessed years ago and have inspired the notion of manned flight?
The Swallow-tailed Kite
http://www.northamptonshirewildlife.co.uk/images/swallowtailedkite.jpg
NOTES:
1.) An airfoil is the shape of a wing or blade of a propeller, rotor or turbine, sail or feather. It is uncertain who discovered the function of the shape, but George Cayley, c1800’s should get a major share of the credit.
http://en.wikipedia.org/wiki/George_Cayley
2.) Archimedes principle states that any body completely or partially submerged in a fluid (gas or liquid) at rest is acted upon by an upward, or buoyant, force the magnitude of which is equal to the weight of the fluid displaced by the body. Source: Encyclopedia Britannica
Archimedes principle is more commonly stated: A body completely, or partially submerged, experiences an upward force equal to the weight of the fluid displaced.
3.) wikipedia presents a straight forward and intuitive definition of Bernoulli’s equation
http://en.wikipedia.org/wiki/Bernoulli’s_principle
4.) In reality, the work of Sir Isaac Newton (the laws of motion, c1687) and the work of Faraday (electricity flows from a moving magnetic field, c1821) are so important that no technologically based civilization could survive handily without them.
5.) Wrights finally took to the air on December 17, 1903, making two flights each from level ground into a freezing headwind gusting to 27 miles an hour. The first flight, by Orville, of 120 feet in 12 seconds, at a speed of only 6.8 mph over the ground. The next two flights covered approximately 175 and 200 feet, by Wilbur and Orville respectively. Their altitude was about 10 ft above the ground.
http://en.wikipedia.org/wiki/Wright_Brothers
6.) Gauge pressure is stated in pounds per square inch, above the atmosphere. Under ordinary conditions the term pressure is understood to mean gauge pressure, the “0” point being that of the pressure of the atmosphere. This system requires pressures below that of the atmosphere to be expressed as a partial vacuum, a complete vacuum being 14.7 pounds below the normal atmospheric pressure. Hence, Absolute pressures are those of the gauge (due to head pressures) plus the additional amount due to the atmosphere.
If gauge pressure = 0 then absolute pressure = 14.7 (psi)
If gauge pressure = 10 then absolute pressure = (10+ 14.7) = 24.7 (psi) absolute
If gauge pressure = 20 then absolute pressure = (20+ 14.7) = 34.7 (psi) absolute
Source:
http://chestofbooks.com/home-improvement/repairs/Mechanics-Household/Gage-Pressure-Absolute-Pressure.html
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