Water fountain - what power is expended to get it to a certain height?

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SUMMARY

The discussion focuses on calculating the power expended by a water fountain that shoots water 10 meters high with a stream diameter of 10 cm. Using the equation for power, the user derived the velocity of the water to be approximately 14.007 m/s and calculated the mass based on the density of water (1000 kg/m³). The final power output was determined to be 10851.8 Watts, using the formula Power = mgh/t, where m is the mass, g is the acceleration due to gravity, and h is the height.

PREREQUISITES
  • Understanding of basic physics concepts, specifically Conservation of Energy.
  • Familiarity with the equations of motion, including v = v0 + at.
  • Knowledge of power calculations in physics, specifically Power = change in work / change in time.
  • Basic understanding of fluid dynamics, particularly the properties of water density.
NEXT STEPS
  • Study the principles of Conservation of Energy in greater detail.
  • Learn about fluid dynamics and the behavior of fluids in motion.
  • Explore the derivation and application of the equations of motion in real-world scenarios.
  • Investigate the relationship between power, work, and energy in mechanical systems.
USEFUL FOR

Students in physics courses, particularly those studying mechanics and fluid dynamics, as well as engineers and anyone interested in the practical applications of power calculations in fluid systems.

Maggie W
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Homework Statement


A fountain shoots a stream of water 10 m up in the air. The base of the stream is 10 cm across. What power is expended to send the water to this height?


Homework Equations


Power = change in work / change in time (Joules / second = Watts)
x - x0 = v0t + 1/2at2
v = v0 + at

The Attempt at a Solution


This question is from chapter 8 (Conservation of Energy) in the extended 3rd edition of "Physics for Engineers and Scientists". The Class is Physics with Calculus I. My professor gave this problem as one of the HW assignments, and we turned in the HW already, but he never goes over any of the questions. Just curious on how to get the answer. This is as far as I could go:
Mass is not given.
Velocity = sq rt of 2gh = 14.007 m/s.
Volume = lwh = 0.1(10)w = w.
Density = m/v = m/w. Density of water = 1000 kg/m3. Mass = dv = 1000w.
Power = [mgh/t] = [1000w(9.81)(10) / t] = [98100w/t].
 
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I got it. The answer is 10851.8 Watts.
 

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