Question - Law of Archimedes

Imagine you have an elevator and we place a bucket filled with water in it. On the surface of the water there is a floating cork, which is in some portion inside the water. What would happen to the cork if the elevator moves up or down? Would it submerge more when moving up, or less when moving down? Or nothing will happen to it's position?

To answer the question we need to consider the Law of Archimedes. If we calculate the total hydrostatic force acting on an immersed body, which is in fact the surface force, we will see that it equals to -G, so it is directed against the gravity force. As a result, its value is equal to the weight of the displaced liquid.

Once the lift generates an increase/decrease in the water's weight, by the acceleration, the displacement force will also be increased/decreased by the same amount. Therefore our body (cork) will stay at the same level in the water.

Archimedes' principle also states that when a body is immersed in a fluid it experiences an upthrust, or apparent loss of weight, equal to the weight of the fluid displaced by the body. Fluid pressure is increasing with depth, which means that there is a greater pressure pushing up on the body from underneath than there is pushing down on it from on top.

Peter Deak

Reference: A.C.Kermode, Mechanics of Flight, 10th edition, pp.25.

Why do birds fly in V shape?

I was wandering about the birds which were flying over my head recently, why do they actually fly like this? I started to think it over and I amazed myself that the answer is just that obvious. To reduce drag!

redorbit.com

Okay, don't get there too fast, so let's consider the air first. It's invisible, therefore making our life's harder. In the case of a ship, when it passes through water we can see the bow wave, wash astern and all the turbulence it creates. When an aeroplane makes its way through air we don't see any difference in the formation of air but we know about the drag. In fact, drag is a defined resistance produces to its motion. Drag determines the efficiency of flight therefore all aircraft are well designed to achieve the least possible resistance with air.  Before moving to birds, there is still another concept I would like to explain. Wakes, which in the case of airplanes are very similar to the wakes made by boats or ships. It's a displacement, as the vehicle passes through this fluid, in one case it's water, in one case it's air. The wingtips are creating wake vortices. It's a very large cone, coming back of the tip of the airplane. If there is a trailing plane which  intersects that cone, you'll feel choppiness.

https://spie.org/x14493.xml

Birds are all smart. They probably have felt the same effect if they fly behind another bird, therefore they are avoiding it. In fact, they are even smarter that they form a V shape, fly in the upwash of the wingtip vortices of the leading bird. The upwash helps them to support their weight, so achieving a reduction in the induced drag. The one flying on the front have the largest possible drag from all, but they all change places in time to have equally distributed flight fatigue among the other birds.

In military aviation it is a very common practice to fly in a V shape, also due to the same reason. In such flights they are doing a so called 'vortex surfing' to reduce drag.

An 26 (photo: István Horváth)

References:

• http://en.wikipedia.org/wiki/V_formation

• A. C. Kermode - Mechanics of Flight

Peter Deak