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## hydromechanics

### 3. Series 24. Year - 1. Warm-Up

• Dr. Nec.

There are two ways to measure the amount of wood in a pile of trees. Either as the volume of pure wood in the pile or as the volume of wood together with the empty spaces in the pile. Find the conversion factor between these two units assuming the trees are cylinders of radius $r$ that are layed one on top of the others.

• Bubbles.

A spherical cap of radius $r$ is made by blowing air into a circular surface of soap water. Estimate the velocity of air molecules hitting the surface?

Jakub

### 3. Series 24. Year - P. Water, water and water

There are many interesting properties of water that other liquids do not possess. Some of them are listed at http://www.btinternet.com/ martin.chaplin/anmlies.html. Think of some consequences of these anomalies for the life on Earth, humans and technology.

Mára was listening to Meteor.

### 1. Series 24. Year - 1. floating sphere

A solid sphere of density ρ is placed between two layers of immiscible liquids (see picture). Densities of the upper and lower liquids are ρ_{1} and ρ_{2} respectively. Assume that ρ_{1} ρ < ρ_{2}. Calculate the fraction of the sphere surrounded by the upper resp. lower liquid.

Z ruských bylin vyčetl Marek

### 1. Series 24. Year - P. to be, or not to be

Two travelers, one fat and the other skinny, are arguing who would have better chances of surviving in extreme conditions. Tell them who will live longer in the following environments. Hot(50 °C), cold(-1 °C), after a boat accident in the Mediterranean sea, inside a hurricane, inside a heavy snow storm and in the middle of earthquake inside a city. Except of their body fat they are exactly the same. They even wear the same clothes and they do not carry anything else. Be original and remember that details matter.

Ve známém televizním pořadu viděl Honza P.

### 6. Series 23. Year - P. tora tora tora

In the middle of the Battle of Midway one of the Japanese pilots got thirsty. After searching the cockpit he found out that the supply management gave him only bottles with soda. What should he do in order to satisfy his thirst?

### 1. Series 23. Year - 4. emptying centrifuge

Lets have a tall cylindrical vessel filled with water (radius $r$, height of water $h)$ and spin it around its axis at angular speed $ω$. At the centre of bottom is a small orifice of surface area $S$, while the vessel is still rotating. How much water will escape the vessel?

Archivní víno.

### 5. Series 22. Year - 3. the Earth

What was the speed of Earth rotation during solidifying of Earth to have the difference between Equator radius and pole radius same as today?

na schůzku donesl Honza Jelínek

### 5. Series 22. Year - E. WC

Measure, how high the water will splash during fall of different bodies onto a water level. Observe the dependence of height, shape and mass of falling object. What percentage of energy is used to create waves on the water level?

na oné místnosti vymyslel Jakub Benda

### 4. Series 22. Year - S. Foucault pendulum and Earth rotation

• Foucault pendulum has drawn into a sand at two different demonstrations two different diagrams, as on the picture. Find out, what caused different shape and how long the pendulum was to create such diagrams on the floor of Paris cathedral. How many tips do the stars have in reality?
• What shape will have the water level in barrel standing still at horizontal plane?
• Show, that equation

$$δf=f_{+}-f_{-}=4**ω**\cdot \textbf{S}/(λ_{0}P)$$ for frequency difference (frequency of beats) of two contra-propagating light beams in laser gyroscope, is valid for any shape of gyroscope, not only circle.

K procvičení probrané látky zadali autoři seriálu.

### 3. Series 22. Year - 1. hydrogen

Fykos organisers were left with a container with compressed hydrogen. And they plan to transfer all hydrogen into a light balloon (so it will have atmospheric pressure). Is such balloon able to lift the container, if the temperature is constant?

Z maďarské přípravy na FO od Dalimila vybral Aleš.