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Example:

Suppose we have a garden hose laid on a concrete floor. This garden hose is made out of rubber and is sealed on both sides. It is completely filled with water with no air bubbles whatsoever.

The outside, inside diameter and length of the hose are known and we assume (for sake of simplicity) that the bulk modulus of water is infinite and the rubber hose doesn't expand or contract under pressure.

Now let's say 70Kg person stands on the hose - what will be the pressure inside the hose?

P.S. This is not a homework - I am puzzled by what happens with the pressure inside the hose as it is a part of thought experiment of mine...

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Air beds and water mattresses are similar examples.

The person standing on the hose will need a force of about 700 N to be exert upwards.

This force will be transmitted over the contact area between the person's soles and the hose. If you know that area you can equate this extra pressure exerted by the soles to the extra pressure that the water in the hose must exert. This will be the pressure of all the water and in places the hose or the ground will counteract the outward force due to the increased water pressure.

However I think that the flaw in this argument is your statement

we assume (for sake of simplicity) that the bulk modulus of water is infinite and the rubber hose doesn't expand or contract under pressure

That statement makes water incapable of reducing in volume and hence the molecules of the water cannot get closer together.
It also means that the rubber cannot stretch to provide a force to counteract the increase in pressure.
In such a case how would adjacent molecules know what each of them is doing? So perhaps it is better not to make those assumptions?

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  • $\begingroup$ The thing is that water transmits the force throughout the hose so my guess is that pressure should be equal to ~700N/inside area of the hose... Just not 100% sure about this... $\endgroup$
    – user2820052
    Commented Jan 29, 2016 at 22:02
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    $\begingroup$ But you need the force of 700 N to be applied over the area of contact of the soles. $\endgroup$
    – Farcher
    Commented Jan 30, 2016 at 1:02
  • $\begingroup$ Yes, but then the pressure is distributed over the surface area of hose's inside... Shouldn't the force inside the hose than be P=700N/inside area?? Or do you reckon its P=700N/(contact area of soles). It's kind of confusing because we also have the concrete 'pushing' against from the other side... $\endgroup$
    – user2820052
    Commented Jan 30, 2016 at 5:50
  • $\begingroup$ The pressure goes up by 700/area of soles. So the force on the inside of the hose due to this increase in pressure goes up by 700/area of soles x inside area of hose. Since that extra 700 N force has to be transmitted to the ground I think that the contact area between the ground and the hose will change. $\endgroup$
    – Farcher
    Commented Jan 30, 2016 at 8:45

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