Hard Hat Rubber

Hard Hat Rubber

The hardest physics/engineering problem ive seen. can anyon answer please?hat would you like to ask?

A pipe one mile in length and with 1-inch inside with diameter is set in the ground such that it is optically straight that is laser beam will pass down the centerline of the whole pipe. The centerline of the pipe is exactly level; that is at right angles with a line passing through the center of the earth. Now, by means of a funnel and rubber tubing. water is poured into one end of the pipe until it flows from the other end. The funnel and tubing are removed and water is allowed to flow freely from the open ends. Neglect the surface tension of the water (it and calculate how much water is left in the pipe. (Hint: The answer is not zero, and take the radius of the earth to be exactly 4000 miles)

The question in not how long will it take the water to flow, but how much is left in the pipe.

The surface of the water will seek the lowest equipotential level, meaning that the water that is left in the pipe will match the curvature of the earth (just like oceans do). So at both ends of the pipe, the level of water is zero, and its surface rises on a radius of 4000 miles until the center of the pipe is reached, where the water height is maximum, and then it curves back down to zero height at the other end of the pipe.

To analyze this problem, look at a horizontal slice of the pipe. Write an equation for the area that is occupied by water. The water height (and thus area) is a function of the distance along the pipe. Then integrate that equation along the length of the pipe (or along the first half of the pipe length and double the result). The answer will be the volume of water remaining in the pipe. Convert to volumetric units of your choice.

By the way, "level" means a curved line or curved surface that is perpendicular to the gravity vector (like the surface of oceans, ignoring tidal effects). The pipe is straight. It is not level anywhere except at the point halfway between the ends of the pipe.

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