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2B30.u1 - Glass of Water and Card

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​2B30.u1 - Glass of Water and Card

Preview
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Title2B30.u1 - Glass of Water and Card
Objective

Demonstrate how a pressure differential can keep water in an Inverted glass.

StatusAvailable
Assembly Instructions

Overview: This demo should be practiced until demonstrator is comfortable with it. A tissue may be substituted for the card, and when carefully inverted will still retain the water in the cup.
 
Instructions: Provide a glass, an index card, and a reservoir of water. Optional: provide a screen.

Setup Time5
Operation Time5
Preview Time5
Operation Instructions

Steps:
1.    Fill glass with water
2.    Cap glass with plate or tissue

3.    Invert
 

Instructions: A glass of water is filled either fully or partially with water and a 3 × 5-inch index card is placed on top. The glass can now be turned over and the card and water will be held in place by atmospheric pressure. The extent to which a card can keep water in an inverted glass depends on the height of the water and the surface created by surface tension between the water and the card.

ExportableYes
Demo on DimeYes
PIRA 200No
Export Instructions (if different)
HazardsNone
Analysis/Information

Overview: In this demonstration a card is placed on a glass of water. When the glass is inverted, the card stays in place and the water does not drain out of the glass. Two effects work together to make this possible:
 
Analysis: Surface Tension:
 
The surfaces of the card and the rim of the glass are not perfectly flat surfaces. When the card is placed on the rim, small gaps are created between the surfaces. Fluid with low surface tension (like alcohol) could pour out via those channels. Fluid with high surface tension, such as water, can form a surface at those gaps. The surfaces are just like the smooth surface of a water droplet, which is also due to surface tension. The surface tension of water creates a boundary between the volume of water and ambient air.
 
The seal created with water between the card and the glass allows the volume of water to equalize pressure with the outside at the surface. This phenomenon is part of why the card and water stay suspended, but is a very unstable system because the surface tension can easily rupture due to perturbations.
 
The stability of surface tension goes down dramatically as area goes up, which is why surface tension alone cannot suspend the water in the glass. We need a rigid material to form part of our surface, and allow the surface tension of the water to fill in the remaining gaps. This is why we use a card.
 
You may have observed the strength of surface tension when you put your finger on a straw and lift it out of water. The pressure of the water is at equilibrium with the ambient pressure, and the surface tension is strong enough to remain intact.
 
Pressure: Air and Water in Glass Case
 
Surface tension completes the surface around the volume of water, but the strength of surface tension alone does not explain why the water is suspended. Another force is contributing to suspending the water: pressure. The atmosphere is very high on Earth, and at sea level it creates air pressure of about 15 psi (pounds per square inch). Pressure is a scalar, which means that it is exerted in all directions at any given location, so the 15 psi is not only pushing down, but also pushing up (you can see where this is going).
 
Water, like air, exerts pressure depending on depth. The depth of the water in this case is a function of the height of the glass. For an average glass of about 15 cm tall, we expect a column of about 10 cm of water in a partially filled glass. This column of water has a pressure gradient of about 0.3 psi; this means that the difference in pressure from the top of the water to the bottom is a difference of 0.3 psi. We know the ambient pressure is 15 psi, so in order for the system to be at equilibrium, the enclosed air bubble must be 14.7 psi.
 
What makes an air bubble change from an original pressure of 15 psi (when it was part of the ambient) to 14.7? Boyle’s Law tells us that when volume increases, pressure decreases, so increasing the volume of the air bubble will reduce the air bubble’s pressure. The desired pressure change from 15 psi to 14.7 represents a 2% change in pressure, which means we need a 2% change in volume. The volume change required for the air bubble we’ve described is a mere millimeter of height displacement. We can change the volume of the system by displacing water in one of two ways:
 
1. Letting water leak out without letting air bubbles in.
2. Letting the card dip below the rim by about a millimeter with a layer of water suspending it, again without allowing bubbles in.
 
Once the water is displaced, the enclosed air bubble will be at the appropriate pressure of 14.7 psi. When that is added to the 0.3 psi gradient contributed by the water, the system is in equilibrium and the surface tension is not strained.
 
Pressure: Only Water in Glass Case
 
When you put your finger on a straw in water, and pull it out, you notice that the water doesn’t evacuate. This same phenomenon explains why we can invert a full glass of water.
 
A full 15 cm glass of water creates a water pressure differential of 0.36 psi. So, when the glass is upright in ambient pressure of 15 psi, surface of the water is at 15 psi and the bottom is at 15.36 psi. When you hold a card on the glass and invert it, the pressure equalizes through the exposed water surface so that the water surface (now on the bottom) is still at the ambient 15 psi, and the top of the water (the now upright bottom of the glass) is at 14.64 psi. Again, there is no pressure difference at the surface between the water and the ambient, so the surface tension is not strained much and doesn’t rupture.
 
Some things to think about:
 
The inverted glass and card are fairly stable for the enclosed bubble case. This is because perturbations that strain the surface also increase the volume of the enclosed air bubble. This is a negative feedback system. If the card displaces from the rim (in a very small way), the enclosed air bubble’s pressure will decrease enough to create a force that attracts the card back to the rim. However, only a slight perturbation is required to rupture the surface and make a big wet mess.
 
The only factor that contributes to the water pressure is the height; this means that the exposed area of the glass does not change the water pressure. In other words, a large mouth glass will present the same pressure as a narrow mouthed glass. But, by increasing the exposed area the surface tension will suffer because it will be spread over a larger area and therefore be less stable.
 
You may be wondering why a glass of water spills at all if these rules of pressure exist between the air and water. The system described above depends on the surface being intact. Once the surface tension is broken, then the rules of density guide the system and air bubbles can displace all the water, making it pour out of the glass. Pressure only works here if there a surface preventing air bubbles from displacing the water.
 
Fun permutation: Rely heavily on surface tension. A tissue paper or fine screen are ideal materials for surface tension to form resilient surfaces upon. With a fine screen the instructor can pour the water through the screen, cover the glass with a card, invert the glass, and then remove the card while still keeping the water in. This demonstration requires practice, so only plan on doing it with a preview. Tissue paper (being porous) works similarly.

Category2 Fluid Mechanics
Subcategory2B - Statics of Fluids
Keywordsfull glass, atmospheric pressure, atmosphere, water, glass, card, pressure, tissue, screen
Construction Information
We ground the glass on the Pyrex container to create an even surface.
 
  
  
coffee cup (or glass cup with smooth edge)
1
index card (or tissue or plastic sheet)
1
water - from the tap