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Quickly Lifting a Plastic Sheet

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What type of experiment is this?

Experimental procedure and explanation:

  • Last time, we tried pulling up a plastic sheet placed on a table, and we found that the plastic sheet could not be lifted, even with a large force (“Sticking a Plastic Sheet to a Table”).
  • This time, we gently place the plastic sheet on top of a piece of tissue paper.
  • First, when we try pulling the plastic sheet up slowly, it comes off easily with a very small force. The difference between this case and the previous one, when we tried to pull up the plastic sheet without the tissue paper, is that in this case, the surface of the tissue paper is uneven, and therefore only a very small area of the tissue paper is in direct contact with the plastic sheet (or the table). The hollow parts that do not contact the adjacent surfaces are at atmospheric pressure, and therefore the plastic sheet can be lifted up with a small force.
  • Next, when we pull the plastic sheet up quickly, it can withstand a very large force, but only for a moment.
  • When the plastic sheet is lifted up quickly, air flows into the gaps formed by the tissue paper. Viscous friction between the plastic sheet (or table) and the tissue paper acts on the flow, and the pressure decreases at the downstream side (near the center of the plastic sheet) as the air flows against this viscous friction. (This is the same principle as flow inside a pipe: see “Large-Diameter Hose and Small-Diameter Hose”.) In addition, the reduced pressure near the center further accelerates the air flowing into the gap. Although the pressure is low near the center, the outside of the sheet is in an atmospheric pressure environment, and a large force is generated by the pressure difference. The effects of both the viscous friction and the acceleration depend on how fast the plastic sheet is lifted: the faster you move the plastic sheet, the larger the generated force.
  • It is a mistake to conclude, “because the flow through the gap is fast, the pressure in the gap is small because of Bernoulli’s theorem.” It is also incorrect to assume that the
    [Note]
    • When considering the forces acting on an object under atmospheric pressure, be sure to consider the pressure on both the front and the reverse sides, rather than on one side only. In this experiment, when we try to quickly open up a gap, an area of low pressure is formed near the center of the bottom side of the plastic sheet; the difference between this low-pressure region and the atmospheric pressure towards the outside of the plastic sheet causes a large force. Simply saying “the top side is pushed down by atmospheric pressure” does not explain why the size of the force changes depending on the speed.
    [Keywords] Flow in a gap, Viscous friction, Added mass
    [Related items] Sticking a Plastic Sheet to a Table, Slowly Dropping Ball, Large-Diameter Hose and Small-Diameter Hose
    [Reference] “Illustrated Fluid Dynamics Trivia,” by Ryozo Ishiwata, Natsume Publishing, P180-181.
    “The Wonders of Flow,” Japan Society of Mechanical Engineering, Kodansha Blue Backs, P182-185, P198-203.
    effect is caused because “the top of the plastic sheet is pushed down by atmospheric pressure.”
Last Update:3.3.2017