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

In summary, this question asks for the power expended to send a stream of water 10 m up in the air with a base of 10 cm. Using the equations for power and velocity, the solution is found to be 10851.8 Watts.
  • #1
Maggie W
2
0

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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  • #2
I got it. The answer is 10851.8 Watts.
 

1. How is the height of a water fountain determined?

The height of a water fountain is determined by the amount of energy or power that is expended to pump the water to a certain height. This can be calculated using the equation E = mgh, where E is the energy or power, m is the mass of the water being pumped, g is the acceleration due to gravity, and h is the height of the fountain.

2. What factors affect the power required to get a water fountain to a certain height?

The power required to get a water fountain to a certain height is affected by several factors, including the height of the fountain, the volume and density of the water, the force of gravity, the type and efficiency of the pump, and any frictional losses in the system.

3. How does the power expended to get a water fountain to a certain height impact the energy consumption?

The power expended to get a water fountain to a certain height directly impacts the energy consumption. The higher the fountain, the more power is required, which in turn leads to higher energy consumption. This is why it is important to consider the height and efficiency of a fountain when designing and installing it.

4. Can the power required to get a water fountain to a certain height be reduced?

Yes, there are ways to reduce the power required to get a water fountain to a certain height. This can be achieved by using a more efficient pump, minimizing frictional losses in the system, and designing the fountain to have a lower height. Additionally, using alternative energy sources such as solar or wind power can also reduce the power consumption.

5. Is it possible to calculate the power required for a water fountain to reach a specific height?

Yes, it is possible to calculate the power required for a water fountain to reach a specific height using the aforementioned equation E = mgh. By knowing the mass of the water being pumped, the desired height, and the efficiency of the pump, the power required can be calculated. However, in real-world scenarios, there may be other factors that can impact the actual power consumption.

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