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## hydromechanics

### (4 points)5. Series 26. Year - P. Prague is flooded!

In 2002 Prague experienced serious floodings. Try to estimate the amount of water that can fit into the Prague subway system. All the important parameters of the subway system like the train sizes, number of stations, length of the tunnels etc. can be found online.

Karel was drowning.

### (5 points)2. Series 26. Year - 5. the U tube

Imagine a U-tube filled with mercury, and a bubble of height $h_{0}$ that floats inside (see the attached picture). Describe what would happen if we changed the surrounding atmosphere in the following ways. Assume that the density of mercury is independent of temperature. The same is valid for the glass the tube is made of. Also assume that the surrounding air behaves as an ideal gas. The initial state of the atmosphere is described by temperature $T_{0}=300K$, and pressure $p_{a}=10\cdot 10^{5}Pa$. Furthermore, assume that the system is in a thermodynamic equilibrium at all times, and that the bubble has a cylindrical shape.

• Both ends of the tube are open, and the temperature doubles.
• Both ends of the tube are closed, and the temperature doubles.
• Only one of the ends of the tube is closed, and the temperature doubles. For each of these cases, determine the new size of the bubble, and the height difference between the mercury columns in the two branches.

Bonus: Repeat the calculation assuming that the volume of mercury grows linearly with temperature.

### (4 points)6. Series 25. Year - 4. intelligent polar bears

A sphere of ice is floating in the Arctic Ocean. Calculate the fraction of its surface that is above the sea level. The density of ice is 917 kg ⁄ m and the density of salty water is 1025 kg ⁄ m.

Dominika chatted in a zoo.

### (2 points)5. Series 25. Year - 1. the flu pill

Some pills against flu dissolve in water making it to fizz. At first the pill is on the bottom of the glass but after a while it rises to the surface. Why?

Lukáš wanted to avoid the flu.

### (2 points)3. Series 25. Year - 2. river ride

Lock is placed in a dam on a river in order for ships to be able to pass through. Assume the river has a flow rate of $Q=200m⁄s$ and that the lock connects places with height difference $H=4\;\mathrm{m}$ and has dimensions $s=100\;\mathrm{m}$, $d=20\;\mathrm{m}$. How many ships per day can this lock transport from the lower place to the higher place if the maximum flow rate in and out of the lock is $Q_{Z}=250m⁄s?$

Napadlo Michala při čtení tajného časopisu.

### 5. Series 24. Year - 1. warm up

• blood sedimentation

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.

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