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## hydromechanics

### (3 points)1. Series 36. Year - 2. we are weighing an unknown object

Let us have an ideal scale which we calibrate with a state standard (ethanol) with a mass $m\_e = 1,000~000~165 kg$ and a density $\rho \_e = 21~535,40 kg.m^{-3}$. By calibration, we mean that after placing the standard on the scale, we assign to the measured value the mass $m\_e$. The unknown object is weighed under the same conditions in which the volume is $V_0 = 3,242~27 dl$. What mass did we measure if we weighed the weight $G = 1,420~12 N$? What is the actual mass of the object? We conduct the experiment at a place with standard gravitational acceleration $g = 9,806~65 m.s^{-2}$ and air density $\rho \_v=1,292~23 kg.m^{-3}$. Take into account that the calibration is linear and that the unloaded scale shows zero.

### (13 points)1. Series 36. Year - E. dense ice

Measure the density of ice.

### (9 points)1. Series 36. Year - P. trains

Estimate the consumption of electrical energy for one trip of the IC Opavan train. The train set consists of seven passenger cars, a 151-series locomotive and is capable of reaching a speed of $v\_{max} = 160 \mathrm{km\cdot h^{-1}}$. For simplicity, consider that all passengers are going from Prague to Opava.

### (7 points)1. Series 35. Year - 4. fall to the seabed

A cylindrical capsule (Puddle Jumper) with a diameter $d = 4 \mathrm{m}$, a length $l = 10 \mathrm{m}$ and with a watertight partition in the middle of its length is submerged below the ocean surface and falls to the seabed at a speed of $v = 20 \mathrm{ft\cdot min^{-1}}$. At the depth $h = 1~200 ft$, the glass on the front base breaks and the corresponding half of the capsule is filled with water. At what speed will it fall now? How long will it take for the capsule to sink to the bottom at the depth $H=3~000 ft$? Assume that the walls of the capsule are very thin against its dimensions.

Dodo watches Stargate Atlantis.

### (5 points)2. Series 34. Year - 3. a car at the bottom of a\protect \unhbox \voidb@x \penalty \@M \ {}lake

There are several movie scenes where a car falls into water together with its passengers. Calculate the torque with which a person must push the door in order to open it at the bottom of a lake if the bottom of the door's frame is $8,0 \mathrm{m}$ deep underwater. Assume that the door is rectangular with dimensions $132 \mathrm{cm} \times 87 \mathrm{cm}$ and opens along the vertical axis.

Katarína likes dramatic scenes on cliffs.

### (3 points)6. Series 33. Year - 2. under pressure

The water level in bath reaches height $15{,} \mathrm{cm}$. The plug has a shape of a conical frustum which perfectly fits the hole in the base of the bath. Its radii of bases are $16,0 \mathrm{mm}$ and $15,0 \mathrm{mm}$ and its mass is $11,0 \mathrm{g}$. What force does the bath bottom act on the plug? Assume that the drain pipe below contains air of atmospheric pressure.

Jindra felt pressure to think simple problems up.

### (12 points)6. Series 33. Year - E. viscosity

Measure viscosity (in $\textrm{Pa}\cdot\textrm{s}$) of two different oils using Stokes' method.

Jáchym stole Jirka's idea to steal this problem from labs.

### (10 points)5. Series 33. Year - S. min and max

*We are sorry. This type of task is not translated to English.*

They had to wait a lot for Karel.

### (5 points)4. Series 33. Year - 3. uuu-pipe

What period of small oscillations will water in a glass container (shown on the picture) have? The dimensions of the container and the equilibrium position of water are shown. Assume that there is room temperature and standard pressure and that water is perfectly incompressible.

Karel was thinking about U-pipes again.

### (3 points)3. Series 33. Year - 1. fountain with nozzle

Let us have a fountain with $N$ nozzles of the same cross section. These nozzles are fed by one pump with constant volumetric flow rate, which leads to water streaming to the height $h$. Find this height in case of all nozzles with the exception of one being blocked.

Lukáš experimented in the town square.