Don't let this problem hose you

Classical Mechanics Level 4

A pumper fire truck is pumping water through a hose. The hose connects to the truck at 1 m above sea level and the hose is held on top of a ladder at 10 m above sea level. The base of the hose, where it connects to the truck, has a diameter of 10 cm, and the nozzle, where the water comes out, has a diameter of 2 cm. The pressure at the base of the hose is 700,000 Pa. How much mechanical energy in Joules does one gram of water gain as it goes from the bottom to the top of the hose?

Details and assumptions

  • The acceleration due to gravity is \(-9.8~m/s^2\).
  • The density of water is \(1~g/cm^3\).
  • You may neglect any viscosity for water.
  • 1 atmosphere is 101,325 Pa.

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