Tuesday, January 26, 2010

Venice versus The Sea

Venice versus The Sea

The Venitians put down roots-on a cluster of islands in a lagoon at the north end of the Adriatic Sea-by driving alder and oak piles into the sandy ground. atop these foundations they built homes and palaces and began a battle against the ceaseless rise and fall of the tides. The city's structure, despite reinforcements, have suffered the assault of brackish water, sea-level rise, and subsidence (sinking)-some five inches in the past century. Excessive pumping of groundwater contributed to subsidence.

The MOSE (acryonim for Modulo Sperimentale Elettromeccanico, in english Experimental Electromechanical Module) project, begun in 2003 and projected to be complete in 2014, will string four barriers made up of 78 floodgates-at a cost of nearly six billion dollars-across the three inlets (left) to Venice's lagoon. The gates, raised when unusually high tides threaten flooding, will block seawater from pouring into the lagoon. Controversial from the start, the project provoked years of political wrangling as well as worries about lagoon ecology.

How it works
  1. Hollow steel gates filled with water lie flat in housing caissons built into the lagoon bed at each inlet.
  2. When a flood is predicted, air is pumped into the gates to displace water and make them bouyant, allowing them to rise within a half hour.
  3. Fully elevated, the gates separate sea from lagoon. When the tide recedes, water flows back into the gates to lower them.


Sunday, January 24, 2010

Buoyancy Archimedes

Some objects, when placed in water, float, while others sink, and still others neither float nor sink. This is a function of buoyancy. We call objects that float, positively buoyant. Objects that sink are called negatively buoyant. We refer to object that neither float nor sink as neutrally buoyant.

The idea of buoyancy was summed up by Archimedes, a Greek mathematician, in what is known as Archimedes Principle: Any object, wholly or partly immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.

From this principle, we can see that whether an object floats or sinks, is based on not only its weight, but also the amount of water it displaces. That is why a very heavy ocean liner can float. It displaces a large amount of water.

Archimedes principle works for any fluid, but as divers we are mainly concerned with two different fluids: fresh water, and salt water. We need to think of fresh water and salt water as two different fluids because equal volumes of fresh water and salt water do not weigh the same. For example, a cubic foot of fresh water weighs approximately 62.4 lbs, while a cubic foot of salt water weighs approximately 64 lbs. The extra weight is because of the dissolved minerals in salt water.

Let's take a moment and look at an object in water and Archimedes Principle. If you place a 1 cubic foot object that weighs 63 lbs into fresh water, the object is displacing 62.4 lbs of water, but weighs 63 lbs. This object will be negatively buoyant - it will sink. It is however being buoyed up with a force of 62.4 lbs, so if we weighed it in the water it would only weigh .6 lbs.

If we put the same object into salt water, it would still weigh 63 lbs, but would be buoyed up by a force of 64 lbs, and it would float. It would be positively buoyant in salt water. To make the object neutrally buoyant in salt water, we would have to add 1 lb of weight to the object without changing its size (without changing is displacement). Then it would weigh 64 lbs, and be buoyed up with a force of 64 lbs, thus being neutrally buoyant.

Let's expand on this and look at an example of putting these ideas to work in a real situation. Suppose you know that a boat had lost an anchor weighing 100 lbs. Measuring a comparable anchor, we find out that the anchor displaces 1/2 cubic feet of water. We will also assume that the anchor was lost in a fresh water lake. You do a dive and find the anchor and want to bring it to the surface but the only resource you have available are some 1 gallon milk jugs. How many would you need to tie on to the anchor to float it to the surface?

At this point we need to do a little simple math. We know that a cubic foot of fresh water weighs 62.4 lbs, so the anchor displacing 1/2 a cubic foot of water would be buoyed up with a force of 31.2 lbs. Let's round this to 31 lbs for simplicity. This means our anchor that weighs 100 lbs on land will weigh 100-31 or 69 lbs in the water. We now know we need enough 1 gallon milk jugs to generate 69 lbs of lift.

Perhaps you remember the old expression "A pint a pound the world around." This refers to the fact that a pint of water weighs about a pound. Since there are 8 pints in a gallon, we know a gallon of water must weigh about 8 lbs. Since we know a cubic foot of water weighs 62.4 lbs, this means there are about 8 gallons of water in a cubic foot. Let's put it together and solve our anchor problem.

If we need 69 pounds of lift, we divide 69 by 8 lbs per gallon to learn we need 8.625 gallons of water displacement to make the anchor neutrally buoyant. This means, we could fill 9-one gallon milk jugs with air to lift our anchor.

Let's try another. A 3 cubic foot object weighing 400 lbs is dropped into the ocean. How big of an air lift bag (in cubic feet) would you need to lift the object?

First we determine that a 3 cubic foot object in salt water would have 3x64 lbs of lift, or 192 lbs of buoyant force. If we subtract 192 from 400 we get 208 lbs. This means we need to generate 208 lbs of lift to make our object neutrally buoyant. We then divide 208 (the objects in water weight) by 64 (the weight of a cubic foot of sea water) to get 3.25 cubic feet of displacement is needed to make the object neutrally buoyant. Thus, we would need at least a 3.25 cubic foot air lift bag.

Friday, January 22, 2010

Cremona Diagram

The Cremona diagram is a graphical method used in statics of trusses to determine the forces in members (graphic statics). The method was created by the Italian mathematician Luigi Cremona.

In the Cremona method, first the external forces and reactions are drawn (to scale) forming a vertical line in the lower right side of the picture. This is the sum of all the force vectors and is equal to zero as there is mechanical equilibrium.

Since the equilibrium holds for the external forces on the entire truss construction, it also holds for the internal forces acting on each joint. For a joint to be at rest the sum of the forces on a joint must also be equal to zero. Starting at joint Aorda, the internal forces can be found by drawing lines in the Cremona diagram representing the forces in the members 1 and 4, going clockwise; VA (going up) load at A (going down), force in member 1 (going down/left), member 4 (going up/right) and closing with VA. As the force in member 1 is towards the joint, the member is under compression, the force in member 4 is away from the joint so the member 4 is under tension. The length of the lines for members 1 and 4 in the diagram, multiplied with the chosen scale factor is the magnitude of the force in members 1 and 4.

Now, in the same way the forces in members 2 and 6 can be found for joint C; force in member 1 (going up/right), force in C going down, force in 2 (going down/left), force in 6 (going up/left) and closing with the force in member 1.

The same steps can be taken for joints D, H and E resulting in the complete Cremona diagram where the internal forces in all members are known.

In a next phase the forces caused by wind must be considered. Wind will cause pressure on the upwind side of a roof (and truss) and suction on the downwind side. This will translate to asymmetrical loads but the Cremona method is the same. Wind force may introduce larger forces in the individual truss members than the static vertical loads.
Taken from http://en.wikipedia.org/wiki/Cremona_diagram

Full Tilt of Pisa's Leaning Towers

Full Tilt of Pisa's leaning towers - yes, there are several-the famous one is the least likely to people. That's because an 11-year restoration effort, involving three years of painstaking soil removal, has successfully steadied the precariously poised campanile.
Pisa's soil is mostly compressible clay and sand, which gives way over time and causes big buildings to shift. The iconic edifice started listing northward during its first phase of construction, in the 1100s, then changed course pitching southward over the next eight centuries.
An 1817 measurement put its incline at 5 degrees: by 1990, the cant had increased to 5.5. Fearing the 197-foot-tall, tourist-luring monument might collapse, italy's premier formed an international team to preserve it.
John Burland, a top project engineer, says the tower's tilt is back to 5 degrees, and "over the last two years, almost no movement has been detected,"The city's other bell towers, though linked to larger structures, haven't been bolstered. One hopes the Learning Tower of Pisa won't someday be the Only Tower of Pisa (National Geographic)