A siphon tube is useful for removing liquid from a tank.

Chapter , Problem 104

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A siphon tube is useful for removing liquid from a tank. The siphon tube is fi rst fi lled with liquid, and then one end is inserted into the tank. Liquid then drains out the other end, as the drawing illustrates. (a) Using reasoning similar to that employed in obtaining Torricellis theorem (see Example 15), derive an expression for the speed v of the fl uid emerging from the tube. This expression should give v in terms of the vertical height y and the acceleration due to gravity g. (Note that this speed does not depend on the depth d of the tube below the surface of the liquid.) (b) At what value of the vertical distance y will the siphon stop working? (c) Derive an expression for the absolute pressure at the highest point in the siphon (point A) in terms of the atmospheric pressure P0, the fl uid density r, g, and the heights h and y. (Note that the fl uid speed at point A is the same as the speed of the fl uid emerging from the tube, because the cross-sectional area of the tube is the same everywhere.)