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There is a hole in the styrofoam cup which has water in it. (A) Direction in which...

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quddoos | Valedictorian

Posted August 12, 2013 at 10:22 AM via web

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There is a hole in the styrofoam cup which has water in it.

(A) Direction in which pressure initally causes water to move as it escapes from the hole  

(B) Direction in which gravity acts on the escaping water

(C) Would the path followed by the water escaping from the hole be different if it the hole were placed higher or lower? Why or why not?

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mvcdc | Student, Undergraduate | (Level 1) Associate Educator

Posted August 12, 2013 at 6:26 PM (Answer #1)

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Hydrostatic pressure is the kind of pressure responsible for the phenomena that is being described in the question. It is the result of the gravitational pull on a liquid causing its molecules to move towards an area of least resistance -- and hence, if you have a hole in a styrofoam cup, the direction would be outwards.

Initially, if you punch a hole on a styrofoam cup field with water, the direction of flow would be outwards along the horizontal. This initial flow is dominantly due to the pressure difference caused by creating the hole. One side of the cup is filled with water (hence you have a high pressure) while the other side is merely open/atmosphere (hence low pressure). This causes the water to flow towards the outside of the cup due to hydrostatic pressure. The force of the liquid above the hole pushes the water below it outwards.

Gravity always acts downwards (or more technically towards the earth's center). This is still true in this case as gravity simply pulls the water molecules downwards. 

At this point, note that the espcaping liquid is being acted upon by two force. The first force is the initial force applied by the pressure difference (the pushing of the other liquid molecules). The second force is the force of gravity which is the constant downward pull on the water molecules. As a result, you would get a parabolic path for the escaping water.

If the hole is punched higher/lower, you would observe a different path for the escaping liquid. Since the force of gravity would be the same, we can attribute the difference on the pressure or the push of the liquid. Note that pressure (in this context; hydrostatic) is given by: `rho = mgh` , where h is the height of the water above your reference point (in this case, the hole). For instance if you punched a hole near the top of the styrofoam cup, the height of the water above, h, would be small, and you would simply observe that the water only appears to flow 'along' the styrofoam cup (parabola with narrow opening). On the other hand, if you punch a hole near the very buttom of the cup, the trajectory would be different as the water would travel further away from the cup (parabola with wider opening).

To summarize, two forces are acting on the escaping liquid. The pressure of the water 'column' above the level of the hole giving it a 'push' outwards, and the force of gravity pulling it down. The resultant of the two would be a parabolic trajectory, the opening of which would depend on the position of the hole, which is essentially the height of the water from the hole and hence the pressure that is exerted by the other molecules on the escaping liquid.


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