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## hydromechanics

### 3. Series 22. Year - E. in vino veritas

Try following experiment: Fill the same glasses one with water, second with wine up to the top. Put a sheet of paper on the glass with water. Then turn the glass with water upside down and face it with the glass with wine (final state is on the figure). Now try to remove the paper and you will see very strange effect: the content of glasses will change, without mixing (it takes a time, be patient). Find out, why it is as it is. How is the time for change dependent on surface area, alcohol concentration and other parameters? Will this happen also for other liquids? E.g. coloured water, milk, oil…

Na přednášce na vlastní oči viděl Jakub M.

### 6. Series 21. Year - 3. cooling a soup

Assume copper hemispherical pot, with diameter of 40 cm. The pot is filled with a soup and is placed in water. It is floating 10cm under water level. Will the water start to fill the pot, if the border of pot is pulled up by a chain by 10 cm?

Sbírka od Dalimila Mazáče.

### 3. Series 21. Year - P. high and low tide

High tide and low tide are caused by tidal forces, mainly gravitational force of the Moon. High tide repeats every 12 hours and 25 minutes, however on the Earth we always see two high tides on opposite sides of the Earth. It means that one high tide circles the Earth in approximately twice the time which is 25 hours. Therefore on the equator of length 40 000 km the high tide is moving at speed approximately 40 000/25 km ⁄ h = 1 600 km ⁄ h. This is even more that the speed of sound in air.

However, from the experience we know, that water in ocean does not move at this speed, at the ships does not shipwreck regularly and bring bananas from Kostarika. Is there some mistake in calculation, or do we have to interpret it differently?

Úlohu navrhl Honza Hradil.

### 2. Series 21. Year - 3. wine is flowing

Wine makers and truck drivers know how to move liquid from heavy containers. Winemaker Ignac wants to move wine from one container to another. First he puts empty container on the ground and full to the level $Δ$. Then both containers are connected by a tube and with help of little suction wine starts to flow to bottom container. How long it will take? Assume, that both containers are same cylinders of radius $R$ and height $H$.

Vymyslel Jano Lalinský.

### 2. Series 21. Year - E. bubo bubo

Verify experimentally following hypothesis: the rotation of Earth causes water on north hemisphere to swirl to right, on south hemisphere to left. For your conclusion to have relevance, enough number of measurements must be done at different conditions.

Napadlo zadat Honzu Prachaře.

### 1. Series 21. Year - 2. save the bubble!

Batyscaphe Trieste dived into deep sea and released a bubble which started to come to the surface. What is the vertical speed of the bubble? How will this speed change? How long it will take to reach surface? What size of bubbles will be fastest?

Úlohu vymyslel Jano Lalinský.

### 6. Series 20. Year - E. blowing experiment

Measure what is the maximum pressure (and underpressure) which can be made by your mouth by blowing and sucking air.

O ruce vás chtěl připravit Michael Komm.

### 5. Series 20. Year - 4. Buffalo Bill and Jessie James

Buffalo Bill is searching for Jessie James, well known bandit. Finaly he found him and in town Clay County they meet in fighting. Buffalo noticed a barrel full of petrol located in between both of them on a trolley. But how to get barrel near to Jessie (to light it up)?

Jessie made a hole in the barrel with his gun in 9/10 of height and the petrol is flowing from the barrel. Buffalo hits the barrel exactly in the middle and shoots again. Calculate what is the acceleration of the barrel and trolley at the beginning and how it depend on the position of the second hole from Bill's revolver. Assume the mass of bullet is negligible.

What height is optimal for petrol to splash to longest distance?

Znovu zadaná úloha V.1 z 18. ročníku, protože tehdejší řešení je špatně. Přílepek od Honzy Hradila.

### 4. Series 20. Year - 1. shopping for mineral water

You may remember buying plastic bottle of your favourite drink in supermarket. The bottle placed on the belt starts spinning trying to stay on the spot. Why this happen?

Analyse following situation: the bottle in rest is placed on the belt perpendicularly to the direction of belt movement.

Suddenly the belt starts moving at constant speed $v=10\;\mathrm{cm}/s$. What will be the speed of the bottle. First analyse following idealisations: (1) approximate bottle by a solid cylinder, (2) the bottle is full of liquid water which does not like to be turned. For simplicity assume negligible viscosity, then include viscosity to your calculations.

Úlohu vymyslel Jano Lalinský na nákupu v TESCU.

### 2. Series 20. Year - 1. Cenek's saw mill

Cenek's saw mill is located at the junction of rivers Vydra and Kremelna in the Boheminan forest (mountains). The saw mill is named after wood retailer Cenek Bubenicek, who has built in 19th century. There is water power plant at its former place declared by state as technical monument.

Power plant uses difference of water levels above and under turbine 10 m, electrical output of power station is 96 kW. Water is distributed to the turbine using rectangular open-top canal. Its width is 1 m, and water is 1,5 m deep. The estimated water speed at the middle of surface is 1 m\cdot s^{− 1}. What is the estimated efficiency of water power station?

Vymyslel Honza Prachař, když byl na výletě na Šumavě.