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If you take a water bottle full of water, and make a hole near the bottom, water obviously spurts out a certain distance. How does the variance of the size of the hole made affect how far and how fast the water spurts out?

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  • $\begingroup$ variance : The quality of being different, divergent, or inconsistent. Do you speak about the size only? Size dependence? $\endgroup$ – jaromrax Feb 5 '18 at 12:39
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    $\begingroup$ You are asking two different questions: One in the title and one in the text. $\endgroup$ – Steeven Feb 5 '18 at 13:21
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The depth of water in the container determines the pressure at the bottom of the container. The speed with which the water spurts from a hole in the container under the action of this pressure is equal to the speed it would possess had it instead fallen freely through a vertical distance equal to the depth of the water at the location of the hole.

But since water has nonvanishing viscosity, the act of forcing it through a hole will slow it down. To first order and for small holes and low pressures, the effect is sufficient to cause the hole to dribble instead of form a jet. The larger the hole, the smaller this effect will be.

Hovever, when the diameter of the hole in the bottom of the container approximates the diameter of the container itself, the water instead tends to simply fall like a dropped weight under the influence of gravity.

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