Lifting Heavy Water By Ancient Time 74 Meter High Water Wheels

[newrobert]

I have one amusement park project where I need to lift heavy water at 200 feet height during amusement park time. Water may be like like 100,000-150,000 liter in one second from the ground pool where water will come back after processed in amusement rides/work etc. I was searching on net to find ways to lift water and I found these ancient time water wheels "norias of hama syria".

http://www.machinerylubrication.com/Read/1294/noria-history

I search how much big pumps I needed to lift this water and I found this general formula. 
 
Pump HP = (height in feet * water flow in gallon per minute)/3960
https://www.easycalculation.com/physics/fluid-mechanics/water-horsepower.php
http://irrigation.wsu.edu/Content/Calculators/General/Required-Water-Pump-HP.php

Normal pump
100,000 liter = 26,417 gallon
26,417 gallon x 60 = 1,585,033 gallon per minute
Pumps HP = (200 * 1,585,033) / 3960 = 80,052
Pumps KW = 59,694 KW Pumps (on 100% efficiency but this will be more at 80%)
Those might be 1000 pumps of 59kw if this formula is correct.
That is huge huge investment or huge power that's impossible for us to bear or install.

Water Wheel Idea
Water wheel diameter = 74 meter
Water wheel diameter = 244 feet
Circumference = 765 feet
Two bucket at both side after every = 6 feet
Total buckets = 127x2 = 254

One bucket size = 4x4x4 feet (64 square feet)
Water in one bucket = 479 gallon
1 Bucket weight = 1,812 kg
Water lifted in one round = 121,603
Wheel speed: 1 round in 2 minutes
Round per minute: .50
Speed: 6.37 feet per second
Speed: 1.942 meter per second
Even this wheel is run by 200 kw motors that's good for us. For example 50kw motors installed at 4 sides to rotate wheel as fast as it can be with safety.

Conclusion:
Other than cost to construct this wheel, is this idea practicable? If not, scientifically what's problem in this idea. I mean same water wheel used thousands years before is constructed at big level and rotated with modern electric motors.

Please advice me. 

 

 

 

[CraigD]

I have one amusement park project where I need to lift heavy water at 200 feet height during amusement park time. Water may be like like 100,000-150,000 liter in one second from the ground pool ...

I search how much big pumps I needed to lift this water and I found this general formula.

Rather than relying entirely on found formulae, it’s good to understand the basic mechanics of the question. They’re contained in these fundamental definitions:

Force = Mass * Acceleration

Work = Force * change in Distance

Power = Work / change in Time

 

Ordinarily, in a simple system without gravity,

Acceleration = change in Velocity / change in Time

 

For a system under constant external acceleration, such as due to gravity, Acceleration is simply that acceleration. For near Earth’s surface, that constant is about 9.8 m/s/s, or for easy estimating, 10 m/s/s.

 

A liter of pure water masses precisely 1 kg.

 

The question, then (taking the smaller number, and keeping everything in metric units), asks the power required to move a 100000 kg mass at an acceleration of 10 m/s/s a distance of 60 m in 1 second. The answer is

100000 kg * 10 m/s/s * 60 m / 1 s = 60000000 W

which agrees with your result of 59694 KW

 

Water Wheel Idea

…

Even this wheel is run by 200 kw motors that's good for us. ...

200000 W doesn’t satisfy the requirements given. Rearranging the formula above, we get

200000 W / (10 m/s/s *60 m) = 333 kg / s

 

Your wheel wouldn't turn fast enough.

 

The key idea here is that the same physical laws described by the formulas of mechanics apply to pumps as apply to water wheels, or tanker trucks, buckets hoisted with ropes, or any scheme you design. Different design have different efficiencies, always less than 100%, so some require more power than others, and all more power than the simple calculations give. No scheme can require less power, because the power describes the act of lifting 100000 kg 60 m in 1 s itself, not how it’s done.

[newrobert]

@ CraigD

 

Thank you for replying and helping me to understand all this.

 

I have one question, will not "circular motion", "centripetal force" or some other forces will not help when big wheel is moving rotating. 

 

For example if you ask 2 people to lift 2 ton car might be they can't but if they try to push the car they can push. Now weight is same but due to circular motion there is some help. What do you say about this?

 

I was thinking that circular motion and some other things will help here. 

 

Robert

[newrobert]

Another question how London Eye 1300 ton wheel is rotated by 150KW motor? What's science behind this?

 

Robert

[CraigD]

Another question how London Eye 1300 ton wheel is rotated by 150KW motor? What's science behind this?

Because the London Eye, like most Ferris Wheels, caries the same mass in each car for a complete revolution.

 

Recall the formula

Work = Force * change in Distance

 

and note that “change in Distance” is a vector, having positive or negative quantity values. In the case of the Ferris wheel, change in Distance is positive for the cars going up, negative and exactly opposite for those going down, so total, net Work = 0.

 

A perfectly mechanically efficient Ferris wheel would need its motor only to begin moving. Of course, no real Ferris wheel or other ordinary machine is 100% efficient, so power is needed to overcome its various frictions. You mention that the London Eye, a very big wheel, requires a 150000 W motor, which seems reasonable – I’ve read travel guides giving 500000 W as its total power consumption, which includes lights, the moving walkway in its boarding area, the individual motors that keep the cars level, etc.

 

A Ferris wheel scheme is no good for a big water elevator like your amusement park project, because you can’t let the wheel carry its loads of water both up and down – you have to dump them on the top.

[newrobert]

Hi CraigD,

 

I am really thankful that you are helping me regarding my project. 

 

1. London Eye total power might be 500KW but driven power is 150KW as I read from their official website.

 

2. As you mentioned to find KW, here I am giving example of 1 bucket, please let me know if that is true.

 

1 Water bucket metal weight = 100 kg

1 One bucket water weight = 6000 kg

 

Total weight = 6100 kg

Gravity = 10 m/s/s

Height/distance = .452 meter

Time = 1 second

Power: 5,514 watts (5.5KW)

 

Above is 1 bucket example that moves up after filling bucket. So one bucket moves .452 meter in 1 second. Is this correct calculation i.e. did I understand your mentioned formula correctly? 

 

Will there not be any difference in required power for one bucket moving 1 feet from pool or 1 feet at 200 feet height. I mean any difference due to height in mass/gravity? 

 

Please help me in both questions. I will calculate each bucket one by one.

 

Robert

[CraigD]

1. London Eye total power might be 500KW but driven power is 150KW as I read from their official website.

You were able to find a better webpage than I was for information about the London Eye. Post its URL (address), so everybody can see it,

 

2. As you mentioned to find KW, here I am giving example of 1 bucket, please let me know if that is true.

 

1 Water bucket metal weight = 100 kg

1 One bucket water weight = 6000 kg

 

Total weight = 6100 kg

Gravity = 10 m/s/s

Height/distance = .452 meter

Time = 1 second

Power: 5,514 watts (5.5KW)

I think your result is 2 times what it should be. Here’s the formula:

(Mass * Acceleration * change in Distance) / change in Time = Power

Here a value for it, using your quantities:

(6100 kg * 10 m/s/s * 0.452 m) / 1 s = 27572 W

 

A couple of details:

1. “weight” is a kind of Force, not a mass. “6100 kg” is a mass, not a force. The weight of the bucket and water is Mass * Acceleration = 6100 kg * 10 m/s/s = 61000 N.

 

2. Because the bucket in your scheme is eventually returned to the pool, the work of lifting it is exactly equal and opposite the work gained by lowering it. So you can ignore the empty mass of the buckets, and any other pieces of the machine involved in raising and lowering them.

 

Will there not be any difference in required power for one bucket moving 1 feet from pool or 1 feet at 200 feet height. I mean any difference due to height in mass/gravity?

If you mean moving the bucket vertically, there will be no difference. The “change in Distance” of changing the height of a bucket from 0 to 1 m is the same as changing it from 60 m to 61 m, so Work is the same.

 

If you mean the work or power needed to move the bucket horizontally, the net work and power is 0, and can be ignored. This is because the work to start the bucket moving horizontally is exactly equal and opposite that taken to stop it. This means you don’t need to worry about the details of the machine used to lift the water – whether it’s a wheel, and Archimedes screw, a pipe, or something else – to calculate the minimum power the system will need.

[newrobert]

Thank you for posting.

 

1. Here is link of London Eye information page 

http://www.londoneye.com/LearningAndDiscovery/Education/TeacherResource/OnlineResource/Main.html

 

Click on "Reference Material" and then "Vital Statistics" and then "Speed".

 

Rotational Motion = Water wheel

I think you are calculating required power as to rotate water wheel assuming weight of water, etc. However exact power to rated water wheel loaded with water buckets can't be calculated until we do calculation as per rotational motion rules. After all water wheel is circulation around axis. So in your given equations are not related with rotational motion. For this we need to find weight of water, weight of rim and spokes because all this is rotating around axis. Right now I can't find wheel structure weight so can't make close idea how much power is required to rotate that water wheel along with water own weight. If we have water wheel rotating structure weight then we will find power to rotate that wheel. What do you say about this?

 

Dropped this idea because in this idea huge water wheel structure weight is also rotating along with water weight that may require additional electricity.

 

Uniform Circular Motion = Roller coaster loop

While searching on Internet I got roller coaster loop idea. I mean instead of building huge water wheel, why not create big o like roller coaster loop where only water buckets are moving in circular path on fixed track. I like this idea because as compare to water wheel idea, in this idea only water buckets are moving and this may take less electricity.

 

For a moment, you forget that water is loaded on buckets and assume there are roller coaster cars of known mass/weight circulating around a circular path. Then how to find required power to rotate these cars in a circle?

 

Can you please give your comments on both i.e. rotational motion (water wheel) and circular motion (roller coaster loop). There should be different formulas to find work/force/torque for linear, rotational or circular motion.

 

I want to do calculation on roller coaster loop idea.

 

Thank you for your help.

Edited November 17, 2014 by newrobert

[CraigD]

While searching on Internet I got roller coaster loop idea. I mean instead of building huge water wheel, why not create big o like roller coaster loop where only water buckets are moving in circular path on fixed track. I like this idea because as compare to water wheel idea, in this idea only water buckets are moving and this may take less electricity.

Regardless of the details of the machine used to lift the given mass of water at the given rate, the power required is at least that given by

Power = (Force * Distance) / time

= ((100000 kg * 10 m/s/s) * 60 m) / 1 s = 60000000 W

 

Some machines are more efficient than others, but none can be more than 100% efficient, so none can use less that 60 MW.

 

My guess is that a noria-style water wheel like you describe in your first post would be one of the most efficient schemes, because its frictional losses are due only to its axel bearing, the friction of the water entering and exiting its buckets, and, because it doesn’t move very fast, a small amount of air resistance on its moving parts. A roller-coaster scheme is similar but has more bearings, so would be less efficient.

 

Modern electric motor-driven turbine pumps and closed pipes are typically about 80% efficient. I suspect this is less efficient than a water wheel. The reason most water pumps for amusement park rides are this type rather than water wheels is that the reduction in energy* use isn’t as important as the ability to conceal the machine, making the park better looking and safer.

 

Can you please give your comments on both i.e. rotational motion (water wheel) and circular motion (roller coaster loop). There should be different formulas to find work/force/torque for linear, rotational or circular motion.

A key concept in mechanical problem like this thread’s is: you don’t have to calculate the many parts and details of a system, just its large, overall behavior.

 

Though it can be good learning and practice to calculate the details, if you’re doing them right, they won’t contradict the initial, overall calculations.

 

* Energy is an important concept in mechanics. It’s a measurement of the ability to do Work. Recall that Work = Force * Distance and Power = Work / Time.