Questions: Answer the following question in as much detail as possible. The figure above represents a method for raising the water from the pond up to the water tower, at a higher level, without using a pump. Water is allowed into the drive pipe, and once it is flowing fast enough, it forces the valve at the bottom closed. Explain how this works in terms of conservation of mass and energy.

Answer the following question in as much detail as possible. The figure above represents a method for raising the water from the pond up to the water tower, at a higher level, without using a pump. Water is allowed into the drive pipe, and once it is flowing fast enough, it forces the valve at the bottom closed. Explain how this works in terms of conservation of mass and energy.
Transcript text: Answer the following question in as much detail as possible. The figure above represents a method for raising the water from the pond up to the water tower, at a higher level, without using a pump. Water is allowed into the drive pipe, and once it is flowing fast enough, it forces the valve at the bottom closed. Explain how this works in terms of conservation of mass and energy.
failed

Solution

failed
failed

Solution Steps

Step 1: Initial state

Initially, the drive pipe is open to the air, and the valve at the bottom is also open. Water from the pond begins to flow down the drive pipe due to gravity.

Step 2: Building Velocity and Momentum

As the water flows down the drive pipe, it gains velocity and therefore momentum due to the "Fall" or the vertical drop from the pond level to the valve's location. This downward flow creates a lower pressure near the valve compared to the still water in the air chamber.

Step 3: Valve Closure

Once the water's velocity is high enough, this pressure difference becomes significant. The higher pressure in the air chamber forces the valve closed.

Step 4: Momentum Transfer and Pressure Increase

With the valve closed, the momentum of the fast-flowing water in the drive pipe is abruptly stopped. This causes a large increase in pressure at the bottom of the drive pipe.

Step 5: Water Forced Upwards

This increased pressure is now higher than the pressure at the top of the water tower. As a result, the water is forced upwards through the discharge pipe into the water tower against gravity.

Step 6: Air Compression and Energy Storage

The air in the air chamber is compressed by the upward-moving water, storing the kinetic energy of the moving water as potential energy in the compressed air. This compressed air acts like a spring, pushing the water further upwards.

Step 7: Cycle Repetition

Once the water flow slows down and the pressure in the drive pipe decreases, the valve opens again. The cycle then repeats, with water flowing down the drive pipe, building momentum, closing the valve, and forcing more water into the tower.

Final Answer:

This system, often called a hydraulic ram, works by converting the potential energy of the falling water in the drive pipe into kinetic energy (velocity of the water). This kinetic energy is then transformed into pressure energy when the valve closes. This high pressure is finally used to lift a portion of the water to a height greater than the pond level by storing the energy temporarily as potential energy in compressed air. The conservation of mass is observed in the total amount of water, some of which flows out through the valve before it closes, while the remaining portion ends up in the water tower. The conservation of energy is illustrated by the continuous conversion of potential energy to kinetic energy, then to pressure energy, and then back to potential energy in the raised water and compressed air.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 37 and a standard deviation of 5. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 32 and 42? ans = %
failedAnswered
The bars in a histogram
failedAnswered
Look at the following passage: No man can fully grasp how far and how fast we have come, but condense, if you will, the 50,000 years of man's recorded history in a time span of but a half-century. Stated in these terms, we know very little about the first 40 years, except at the end of them advanced man had learned to use the skins of animals to cover them. Then about 10 years ago, under this standard, man emerged from his caves to construct other kinds of shelter. Only five years ago man learned to write and use a cart with wheels. Christianity began less than two years ago. The printing press came this year, and then less than two months ago, during this whole 50year span of human history, the steam engine provided a new source of power. Newton explored the meaning of gravity. Last month electric lights and telephones and automobiles and airplanes became available. Only last week did we develop penicillin and television and nuclear power, and now if America's new spacecraft succeeds in reaching Venus, we will have literally reached the stars before midnight tonight. This is a breathtaking pace, and such a pace cannot help but create new ills as it dispels old, new ignorance, new problems, new dangers. Surely the opening vistas of space promise high costs and hardships, as well as high reward. What is the implied main idea? Humans have developed at a very fast pace in comparison to the history of the world.
failedAnswered
On a separate sheet of paper, write out the problem using all the steps. Round using significant figures. How many moles of water are produced when 7.60 moles of propane (C3H8) combust in the presence of oxygen? C3H8 + O2 → CO2 + H2O
failedAnswered
4. domain 5. range 6. x-intercept(s) 7. y-intercept(s) 8. interval(s) where the graph is positive 9. interval(s) where the graph is decreasing 10. interval(s) where the graph is increasing 11. rate of change on [-1,4]