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Richard Lawson
Bolton, Greater Manchester, UK
The cleaning effect depends on the energy transferred from the water to the jar when they collide. Kinetic energy is proportional to mass and the square of the velocity. So, if there is no water in the jar, the mass is zero and there is no kinetic energy. If the jar is full, there is no room for the water to move, so the relative velocity is zero and, again, there is no kinetic energy transfer. There must be an optimum somewhere between.
I have assumed a simple model where the jar is shaken vigorously up and down with a sinusoidal, wavy motion. As the jar moves up, the water is in the bottom and moves up with it. But when the jar starts to move down, the water continues upwards until it hits the top of the jar, thus cleaning the top. The water is then propelled down with the jar until it hits the bottom, by which time the jar is moving up again, thus cleaning the bottom of the jar. My analysis of this motion is too long to reproduce here, but it shows that for maximum energy transfer, the jar needs to be two-thirds full of water. That gives the optimum cleaning. The amplitude of shaking is also important: it needs to be 42 per cent of the jar height to give the correct timing.
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The cleaning effect of water inside a glass jar depends on the energy transferred from the water to the jar when they collide
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Although this model simplifies the real situation, I have used this result myself for several years and found it to work well in practice.
Robin Shipp
Bristol, UK
Shaking water in the jar results in a slug of water moving and dislodging the contents by the kinetic energy of the slug. Kinetic energy depends on mass and velocity, and these two quantities are in opposition: more water provides more mass, but less water provides more room to accelerate the slug. Given that kinetic energy is proportional to velocity squared, I always fill a jar to one-third.
Ian Tindal
Seaton, Cornwall, UK
A quick search for “different shapes of jar” reveals a fascinating diversity with potentially differing internal hydrodynamics. Then there is the question of what substance the jar contains. An additive, such as sand or a surfactant, might be needed in some situations. I fear there isn’t just one possible answer.
Tony Durham
Brighton, UK
Washing with the jar half-full usually gives a satisfactory result. Results with the jar half-empty can be disappointing.
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