53

The volume of the bottle and the volume of the liquid are the same both ways. By subtraction, the means the gas volume is the same either way. The difference assumes in the question’s reasoning doesn’t exist. There is more area in the sideways case. That’ll let equilibrium be reached more quickly. But it’ll reach the same equilibrium either way.


41

In an unopened 2L polyethylene terephathalate (PETE) bottle of soda the primary loss of CO2 is by diffusion of the CO2 through the walls of the plastic bottle. If you left a full bottle at room temperature, the half life of this process is about six months, meaning that a six-month old room temperature bottle of soda will be ~50% flat, even if you never ...


31

Imagine that the air in the atmosphere was just somehow sitting there unpressurised. What would happen? Well, Earth's gravity would be attracting all that air towards the centre. So the air would start to fall downwards. The very bottom layer of air would be prevented from falling through the solid surface, as the air molecules rebound off the molecules of ...


27

Is the weight of the aircraft flying in the sky transferred to the ground? Yes, at approximately the speed of sound. Is the weight of people swimming in the pool also transferred to the ground? Yes How to prove it? The swimming one can be quantitatively proven with a kitchen scale. Weigh an object that will float. Fill a bowl partway with water. ...


14

According to Henry's law the mass of gas dissolved is proportional to the pressure on top of the liquid. Because the pressure is the same in both cases, it should not matter if the bottle is vertically or horizontally


10

If the planes flew higher, to avoid air friction and at much greater speeds, they would orbit, and no weight would be transferred to the ground. But at 900 km/h, the centripetal acceleration (V$^2$/R) is about 1% of g. So its weight is 99% transferred. The weight of floating objects on water is obviously transferred. Just put lots of ice on a water jar to ...


9

I think it is misleading to explain air pressure as the weight of the air column above our head acting per unit area. Actually your head only feels those air molecules which are directly hitting the surface of your head. You don't feel any air molecules which are further away. As explained in Wikipedia - Kinetic theory of gases - Pressure and kinetic ...


5

Yes the supporting force is ultimately transferred to the ground, for a theoretical "proof" (=calculation) one would likely employ the concept of control volume in fluid dynamics, and calculate the momentum balance and pressure balance around the surface of the control volume. Airplane in stable horizontal flight: In simple terms, the pressure ...


4

In short, this is because the surface of an ice cube is wet, i.e, made of a liquid layer. You can bind the scotch tape to its water molecules close by, but they will flow away from the rest of the liquid layer easily, preventing you from transmitting a pulling or shearing force between the scotch tape and the ice cube. The reason for this liquid film is ...


4

The water above applies pressure according to it's depth, the water below always has greater depth, so applies greater pressure. If the cylinder's weight is less than the difference in the upper and lower pressures, then it will be pushed upwards. In other words if the cylinder weighs less than the same volume of water, it's displacement, it will float up ...


4

Consider blocks of equal mass, stacked on each other. The block at the top ‘feel’ the force of gravity and normal force from the block below. The block just below feels force of gravity (it’s weight) plus the force acting from the box above by Newton’s $3^\mathrm{rd}$ Law (if it ‘provides’ normal force on box A, box A acts on it with equal magnitude, but ...


3

Answers in words have already been posted, but perhaps an answer with equations may also help, so I will add this. Consider a thin slice of fluid, whether liquid or gas, in a uniform gravitational field. Say the bottom of the slice is at height $z$ and the top at height $z + w$ where the width $w$ will be small (you can call it $\delta z$ if you like). The ...


3

The pressure increase with depth has nothing to do with compressibility nor molecular level physics. It is simply the total weight of the fluid column above you that increases with depth. Take a water column from Earth, put it on Mars, and on the bottom you will have less pressure, due to the lower surface gravity, hence weight of the column. The ...


2

In one of the adiabatic stroke in the Carnot cycle, the temperature of the gas reduces from T1(to what it was initially heated) to T2(temperature of the surrounding). To be clear, you are describing the reversible adiabatic (isentropic) expansion process that follows the reversible isothermal (constant temperature) expansion process. For the isothermal ...


2

but the water column below is applying a force equals to $-(\pi r^2 h \rho _{water} g +W_{object})$ (via Newton's third law) This isn't true. Unlike a solid surface which would have applied an equal and opposite reaction under equilibrium, for incompressible fluids the situation is different as they displace and deform.* The displaced liquid tends to push ...


2

I would like to comment on your argument that says that when it is upright, despite the same volume, the surface is smaller, hence the pressure. This is where your reasonning is flawed. Indeed in your bottle, the pressure at the end is going to depend on the volume and temperature, not the surface area with the liquid. Surface area with the liquid would ...


2

The pressure difference in both the cases is due to the surface tension of water. Let me explain. Whenever a fluid(let's say $F$) has a surface which is exposed to another medium($M$), the particles on the surface experience forces due to two types of particles, namely, the particles of $F$(cohesion forces) and the particles of $M$(adhesion forces). ...


2

You don't feel the air pressure of the air around you (and hence don't feel the "weight" of air above you) because the pressure inside your body is pushing out with the same force (assuming you're breathing normally). This is different from, say, what you would experience if you held your breath and dove 20 feet down into the ocean -- then you'd be able to ...


2

Please read up on pressure here, and how it is derived in the kinetic theory of gases here , third page. This illustrates the motion of molecules in a gas in a closed container, the kinetic energy of all those molecules impinging on the walls and bouncing off each other and back scattering gives the pressure on the walls for the given temperature and ...


2

The pressure is impulse the air molecules give you in collision on unit area and therefore depends on their speed and density. For simplicity, i will consider only density (this would mean that air column has everywhere the same temperature. This is not true for our atmosphere, but such scenario could be achieved in a lab). Because of gravitation, the ...


2

According to PRL, v.88 (2002), 235502-1, the required pressure is 10-20Mbar (see their Fig. 4). They used laser-driven shock waves.


2

Flying Aircraft Logically: the aircraft is supported by reactions with the surrounding air; the air is supported by the ground, so yes, the weight of a flying aircraft is transferred to the ground. Although winged aircraft fly due to aerodynamics, interactions between air molecules ultimately represent the weight of the aircraft in their interactions with ...


2

This seems like an application of Newton's Third Law: For each action there is an equal and opposite reaction. The airplane flies because the air beneath it exerts an upward force on the wings. There's also a downward force from the air above, but the wing shape takes advantage of Bernouli's principle so that the upward force will be greater. The net force ...


1

The very top air molecule of our atmosphere is attracted by gravity. So it has a weight. The second-top-most molecule thus must carry the weight of the top-most molecule. The third-top-most molecule must hold back against both the force on the second-top-most molecule as well as the weight of it - so it must carry two air molecule weights. The forth-top-...


1

Imagine A very tall square bottomed container of 1 unit "floor" area. A weighing device in the bottom of the container that weighs objects placed into the container. The availability of a number of 1 unit a side cubes each of 1 unit mass. Add one cube to the container - the weighing device will show one unit weight. Add a total of 10 cubes -> 10 units ...


1

Pressure is the consequence of gas particle colliding with the walls of the container, or in this case with you. Gas particles are encouraged to collide with you by other particles that do not have direct contact with you. Particle hits you and bounces back, then the particle hits other particle, bouncess off it and it may hit you again. The higher ...


1

For a massless, frictionless piston, according to Newton's 2nd law, the external force per unit area exerted by the gas on the piston is always equal to the force per unit area $P_{ext}$ exerted by the surroundings on the piston. If the deformation is quasi-static and reversible, the force per unit area of the gas is also equal to the gas pressure ...


1

$$dW = P_{external} dV$$ Work done on a gas is dependent only on the external pressure applied to the gas, which is constant (equal to $P_{atmosphere}$ ) in most cases. It is only in quasistatic processes that $P_{external} = P_{gas}$ at every step of the process. Unless it is mentioned take $\Delta W = P_{atmosphere} \Delta V$ to find out the work done.


1

1) You answer it yourself, the total reaction force is zero at every point, regardless of position, so a non-rigid object will not deform 2) If the sphere is rigid, the shell will not move inwards, but if it is made of individual particles, it will start (or try) moving inwards, which will create a pressure on inward shells, but this pressure will not be ...


1

When you apply two antiparallel equal forces to a non-rigid body, it changes its shape, but what does it mean? It means that different parts of the body start to move with respect to each other, while keeping the center of mass still (because the net force is zero). Let's consider a tiny chunk of matter from the non-rigid body. Before the deformation it was ...


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