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Classical Mechanics

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Density and Pressure: Maximum Water Height

CLMECH-DFI9J9

Water flows through a pipe that starts out with a 6.00 cm diameter and then narrows to a diameter of 2.00 cm with a volume flow rate of 28.27 L/s. The pressure in the 6.00 cm diameter pipe is 6.00 $\times 10^6$ Pa. Both pipe sections are horizontal and the centers of both sections of pipe are at the same height.

A small hole is drilled in each section of pipe (in the 6.00 cm diameter section and the 2.00 cm diameter section) such that the water shoots vertically upward. Assume that the amount of water leaving the pipe through either hole is insignificant and neglect any viscosity of the water or air resistance. Designate the maximum height of the water from the hole in the 6 cm diameter section as $h_{6\,cm}$ and similarly the maximum height of the water leaving the other hole as $h_{2\,cm}$.