>>Pressure and force of pressure
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Why does a person standing on skis not fall into loose snow? Why does a car with wide tires have more flotation than a car with regular tires? Why does a tractor need caterpillars? We will find out the answer to these questions by getting acquainted with the physical quantity called pressure.
Solid body pressure
When a force is applied not to one point of the body, but to many points, then it acts on the surface of the body. In this case, one speaks of the pressure that this force creates on the surface of a solid body.
In physics, pressure is a physical quantity that is numerically equal to the ratio of the force acting on a surface perpendicular to it to the area of this surface.
p = F/S ,
where R - pressure; F - force acting on the surface; S - surface area.
So, pressure occurs when a force acts on a surface perpendicular to it. The magnitude of the pressure depends on the magnitude of this force, and is directly proportional to it. The greater the force, the greater the pressure it creates per unit area. The elephant is heavier than the tiger, so it exerts more pressure on the surface. The car pushes against the road with more force than the pedestrian.
The pressure of a solid body is inversely proportional to the surface area on which the force acts.
Everyone knows that walking in deep snow is difficult due to the fact that the legs constantly fall through. But skiing is pretty easy. The thing is that in both cases a person acts on the snow with the same force - the force of gravity. But this force is distributed over surfaces with different areas. Since the surface area of the skis is larger than the area of the soles of the boots, the weight of a person in this case is distributed over a larger area. And the force acting per unit area is several times smaller. Therefore, a person standing on skis puts less pressure on the snow and does not fall into it.
By changing the surface area, you can increase or decrease the amount of pressure.
When going on a hike, we choose a backpack with wide straps to reduce pressure on the shoulder.
To reduce the pressure of the building on the ground, increase the area of \u200b\u200bthe foundation.
Truck tires are made wider than passenger car tires so they exert less pressure on the ground. For the same reason, a tractor or tank is made on tracks, and not on wheels.
Knives, blades, scissors, needles are sharpened sharply so that they have the smallest possible area of \u200b\u200bthe cutting or piercing part. And then even with the help of a small applied force, a lot of pressure is created.
For the same reason, nature has provided animals with sharp teeth, fangs, and claws.
Pressure is a scalar quantity. In solids, it is transmitted in the direction of the force.
The unit of force is newton. The area unit is m 2 . Therefore, the unit of pressure is N/m 2 . This value in the international system of units SI is called pascal (Pa or Ra). It got its name in honor of the French physicist Blaise Pascal. A pressure of 1 pascal causes a force of 1 newton acting on a surface of 1 m 2 .
1 Pa = 1N/m2 .
Other systems use units such as bar, atmosphere, mmHg. Art. (millimeters of mercury), etc.
Pressure in liquids
If in a solid body pressure is transmitted in the direction of the force, then in liquids and gases, according to Pascal's law, " any pressure exerted on a liquid or gas is transmitted in all directions without change ».
Let's fill a ball with tiny holes connected to a narrow tube in the form of a cylinder with liquid. Let's fill the ball with liquid, insert the piston into the tube and start moving it. The piston presses on the surface of the liquid. This pressure is transmitted to every point of the fluid. Liquid begins to pour out of the holes in the ball.
Filling the balloon with smoke, we will see the same result. This means that in gases pressure is also transmitted in all directions.
The force of gravity acts on the liquid, as on any body on the surface of the Earth. Each layer of liquid in the container creates pressure with its own weight.
This is confirmed by the following experiment.
If water is poured into a glass vessel, instead of the bottom of which has a rubber film, then the film will sag under the weight of water. And the more water there is, the more the film will bend. If we gradually immerse this vessel with water into another container, also filled with water, then as it sinks, the film will straighten. And when the water levels in the vessel and container are equal, the film will straighten completely.
At the same level, the pressure in the liquid is the same. But with increasing depth, it increases, since the molecules of the upper layers exert pressure on the molecules of the lower layers. And those, in turn, put pressure on the molecules of the layers located even lower. Therefore, at the lowest point of the tank, the pressure will be the highest.
The pressure at depth is determined by the formula:
p = ρ g h ,
where p - pressure (Pa);
ρ - liquid density (kg / m 3);
g - free fall acceleration (9.81 m/s);
h - height of the liquid column (m).
It can be seen from the formula that the pressure increases with depth. The lower the submersible descends in the ocean, the more pressure it will experience.
Atmosphere pressure
Evangelista Torricelli
Who knows, if in 1638 the Duke of Tuscany had not decided to decorate the gardens of Florence with beautiful fountains, atmospheric pressure would not have been discovered in the 17th century, but much later. We can say that this discovery was made by accident.
In those days, it was believed that the water would rise behind the piston of the pump, because, as Aristotle said, "nature does not tolerate emptiness." However, the event was not successful. The water in the fountains really rose, filling the resulting "void", but at a height of 10.3 m it stopped.
They turned to Galileo Galilei for help. Since he could not find a logical explanation, he instructed his students - Evangelista Torricelli and Vincenzo Viviani conduct experiments.
Trying to find the cause of the failure, Galileo's students found out that different liquids rise behind the pump to different heights. The denser the liquid, the lower the height it can rise. Since the density of mercury is 13 times that of water, it can rise to a height 13 times less. Therefore, they used mercury in their experiment.
In 1644 the experiment was carried out. The glass tube was filled with mercury. Then it was thrown into a container, also filled with mercury. After some time, the column of mercury in the tube rose. But he did not fill the entire tube. There was an empty space above the mercury column. It was later called the "Torricellian void". But mercury did not pour out of the tube into the container either. Torricelli explained this by the fact that atmospheric air presses on mercury and keeps it in the tube. And the height of the mercury column in the tube shows the magnitude of this pressure. This was the first time atmospheric pressure was measured.
The atmosphere of the Earth is its air shell, held near it by gravitational attraction. The gas molecules that make up this shell are constantly and randomly moving. Under the influence of gravity, the upper layers of the atmosphere press on the lower layers, compressing them. The lowest layer near the Earth's surface is compressed the most. Therefore, the pressure in it is the greatest. According to Pascal's law, it transmits this pressure in all directions. It is experienced by everything that is on the surface of the Earth. This pressure is called atmospheric pressure .
Since atmospheric pressure is created by the overlying layers of air, it decreases with increasing altitude. It is known that high in the mountains it is less than at the foot of the mountains. And deep underground it is much higher than on the surface.
Normal atmospheric pressure is the pressure equal to the pressure of a column of mercury 760 mm high at a temperature of 0 o C.
Atmospheric pressure measurement
Since atmospheric air has a different density at different heights, the value of atmospheric pressure cannot be determined by the formulap = ρ · g · h . Therefore, it is determined using special instruments called barometers .
Distinguish between liquid barometers and aneroids (non-liquid). The operation of liquid barometers is based on the change in the column of liquid level under the pressure of the atmosphere.
The aneroid is a sealed container made of corrugated metal, inside which a vacuum is created. The container contracts when the atmospheric pressure rises and straightens when it is lowered. All these changes are transmitted to the arrow by means of a springy metal plate. The end of the arrow moves along the scale.
By changing the readings of the barometer, one can assume how the weather will change in the coming days. If the atmospheric pressure rises, then clear weather can be expected. And if it goes down, it will be cloudy.
To understand what pressure is in physics, consider a simple and familiar example. Which?
In a situation where we need to cut a sausage, we will use the sharpest object - a knife, and not a spoon, comb or finger. The answer is obvious - the knife is sharper, and all the force applied by us is distributed along the very thin edge of the knife, bringing the maximum effect in the form of separation of a part of the object, i.e. sausages. Another example - we are standing on loose snow. Legs fail, walking is extremely uncomfortable. Why, then, do skiers rush past us with ease and at high speed, without drowning and not getting entangled in the same loose snow? It is obvious that snow is the same for everyone, both for skiers and for walkers, but the effect on it is different.
With approximately the same pressure, that is, weight, the surface area pressing on the snow varies greatly. The area of skis is much larger than the area of the sole of the shoe, and, accordingly, the weight is distributed over a larger surface. What helps or, on the contrary, prevents us from effectively influencing the surface? Why does a sharp knife cut bread better, and flat wide skis hold better on the surface, reducing penetration into the snow? In the seventh grade physics course, the concept of pressure is studied for this.
pressure in physics
The force applied to a surface is called pressure force. And pressure is a physical quantity that is equal to the ratio of the pressure force applied to a specific surface to the area of this surface. The formula for calculating pressure in physics is as follows:
where p is pressure,
F - pressure force,
s is the surface area.
We see how pressure is denoted in physics, and we also see that with the same force, the pressure is greater when the support area, or, in other words, the contact area of interacting bodies, is smaller. Conversely, as the area of support increases, the pressure decreases. That is why a sharper knife cuts any body better, and nails driven into a wall are made with sharp tips. And that is why skis hold on the snow much better than their absence.
Pressure units
The unit of pressure is 1 newton per square meter - these are quantities already known to us from the seventh grade course. We can also convert pressure units N / m2 to pascals, units of measurement named after the French scientist Blaise Pascal, who derived the so-called Pascal's Law. 1 N/m = 1 Pa. In practice, other units of pressure are also used - millimeters of mercury, bars, and so on.
In diving practice, one often encounters the calculation of mechanical, hydrostatic and gas pressure of a wide range of values. Depending on the value of the measured pressure, different units are used.
In the SI and ISS systems, the unit of pressure is the pascal (Pa), in the MKGSS system - kgf / cm 2 (technical atmosphere - at). Torah (mm Hg), atm (physical atmosphere), m of water are used as non-systemic units of pressure. Art., and in English measures - pounds / inch 2. Relationships between different pressure units are given in Table 10.1.
Mechanical pressure is measured by the force acting perpendicular to the unit surface area of the body:
where p - pressure, kgf / cm 2;
F - force, kgf;
S - area, cm 2.
Example 10.1. Determine the pressure that the diver exerts on the deck of the vessel and on the ground under water when he takes a step (i.e. stands on one leg). The weight of a diver in equipment in the air is 180 kgf, and under water 9 kgf. The area of the sole of the diving galoshes is taken to be 360 cm 2. Solution. 1) The pressure transmitted by the diving boots to the deck of the ship, according to (10.1):
P \u003d 180/360 \u003d 0.5 kgf / cm
Or in SI units
P \u003d 0.5 * 0.98.10 5 \u003d 49000 Pa \u003d 49 kPa.
Table 10.1. Relationships between different units of pressure
2) The pressure transmitted by diving galoshes to the ground under water:
or in SI units
P \u003d 0.025 * 0.98 * 10 5 \u003d 2460 Pa \u003d 2.46 kPa.
hydrostatic pressure liquid everywhere perpendicular to the surface on which it acts, and increases with depth, but remains constant in any horizontal plane.
If the surface of the liquid does not experience external pressure (for example, air pressure) or it is not taken into account, then the pressure inside the liquid is called excess pressure.
where p is the liquid pressure, kgf/cm 2 ;
p is the density of the liquid, gf "s 4 / cm 2;
g - free fall acceleration, cm/s 2 ;
Y is the specific gravity of the liquid, kg/cm 3 , kgf/l;
H - depth, m.
If the surface of the liquid experiences external pressure the pressure inside the liquid
If atmospheric air pressure acts on the surface of a liquid, then the pressure inside the liquid is called absolute pressure(i.e. pressure measured from zero - full vacuum):
where B - atmospheric (barometric) pressure, mm Hg. Art.
In practical calculations for fresh water, take
Y \u003d l kgf / l and atmospheric pressure p 0 \u003d 1 kgf / cm 2 \u003d \u003d 10 m of water. Art., then the excess water pressure in kgf / cm 2
and the absolute water pressure
Example 10.2. Find the absolute pressure of sea water acting on a diver at a depth of 150 m if the barometric pressure is 765 mm Hg. Art., and the specific gravity of sea water is 1.024 kgf / l.
Solution. Absolute pressure of the ox by (10/4)
estimated value of absolute pressure according to (10.6)
In this example, the use of the approximate formula (10.6) for the calculation is quite justified, since the calculation error does not exceed 3%.
Example 10.3. In a hollow structure containing air under atmospheric pressure p a \u003d 1 kgf / cm 2, located under water, a hole was formed through which water began to flow (Fig. 10.1). What pressure force will the diver experience if he tries to close this hole with his hand? The area "At the cross section of the hole is 10X10 cm 2, the height of the water column H above the hole is 50 m.
Rice. 9.20. Observation chamber "Galeazzi": 1 - eye; 2 - cable recoil device and cable cut; 3 - fitting for telephone input; 4 - hatch cover; 5 - upper porthole; 6 - rubber attachment ring; 7 - lower porthole; 8 - camera body; 9 - oxygen cylinder with a pressure gauge; 10 - emergency ballast return device; 11 - emergency ballast; 12 - lamp cable; 13 - lamp; 14 - electric fan; 15-phone-microphone; 16 - battery; 17 - regenerative working box; 18 - hatch cover porthole
Solution. Excessive water pressure at the hole according to (10.5)
P \u003d 0.1-50 \u003d 5 kgf / cm 2.
Pressure force on the diver's hand from (10.1)
F \u003d Sp \u003d 10 * 10 * 5 \u003d 500 kgf \u003d 0.5 tf.
The pressure of the gas contained in the vessel is distributed evenly, if we do not take into account its weight, which, given the dimensions of the vessels used in diving practice, has an insignificant effect. The magnitude of the pressure of a constant mass of gas depends on the volume it occupies and the temperature.
The relationship between the pressure of a gas and its volume at a constant temperature is established by the expression
P 1 V 1 = p 2 V 2 (10.7)
Where p 1 and p 2 - initial and final absolute pressure, kgf / cm 2;
V 1 and V 2 - initial and final volume of gas, l. The relationship between the pressure of a gas and its temperature at a constant volume is established by the expression
where t 1 and t 2 are the initial and final gas temperatures, °C.
At constant pressure, a similar relationship exists between the volume and temperature of the gas
The relationship between pressure, volume and temperature of a gas is established by the combined law of the gaseous state
Example 10.4. The capacity of the cylinder is 40 l, the air pressure in it is 150 kgf / cm 2 according to the manometer. Determine the volume of free air in the cylinder, i.e., the volume reduced to 1 kgf / cm 2.
Solution. Initial absolute pressure p \u003d 150 + 1 \u003d 151 kgf / cm 2, final p 2 \u003d 1 kgf / cm 2, initial volume V 1 \u003d 40 l. Free air volume from (10.7)
Example 10.5. The manometer on the oxygen cylinder in a room with a temperature of 17 ° C showed a pressure of 200 kgf / cm 2. This cylinder was transferred to the deck, where the next day at a temperature of -11 ° C, its readings decreased to 180 kgf / cm 2. An oxygen leak was suspected. Check if the suspicion is correct.
Solution. Initial absolute pressure p 2 \u003d 200 + 1 \u003d \u003d 201 kgf / cm 2, final p 2 \u003d 180 + 1 \u003d 181 kgf / cm 2, initial temperature t 1 \u003d 17 ° C, final t 2 \u003d -11 ° C. Estimated final pressure from (10.8)
Suspicions are unfounded, since the actual and calculated pressures are equal.
Example 10.6. A diver under water consumes 100 l / min of air compressed to a pressure of a diving depth of 40 m. Determine the flow rate of free air (i.e., at a pressure of 1 kgf / cm 2).
Solution. Initial absolute pressure at immersion depth according to (10.6)
P 1 \u003d 0.1 * 40 \u003d 5 kgf / cm 2.
Final absolute pressure P 2 \u003d 1 kgf / cm 2
Initial air flow Vi = l00 l/min.
Free air flow according to (10.7)
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