Mechanical energy/efficiency problem

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In summary, the speed of the water just before striking the turbine blades is 41.5 m/s and the rate at which mechanical energy is transferred to the turbine blades with 55% efficiency is 500.704 kJ/s.
  • #1
Flatshoe
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Homework Statement



(i)Water flows over a dam at the rate 580kg/s and falls vertically 88m before striking the turbine blades. Calculate the speed of the water just before striking the turbine blades (SOLVED) and (ii) the rate at which mechanical energy is transferred to the turbine blades assuming 55% efficiency.

Homework Equations



Ek = 1/2mv^2 Mechanical efficiency = Work out/Work in

The Attempt at a Solution


Answer to part (i) v=sqrt2gh

v = 41.5 m/s


Mechanical efficiency = work out/work in

Work out = Ek1 - Ek2

Work in = Ek1 - Ek2/55%



Ok and I'm pretty much stuck. :(

Thanks in advance for any help guys!
 
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  • #2
This problem looks familiar did you post it on some other message board?

As you stated the mechanical energy is the ratio of the work out to the work in. What's the work in? The efficiency is 55% so, 55% of the work in is returned.
 
  • #3
Squeezebox said:
This problem looks familiar did you post it on some other message board?

As you stated the mechanical energy is the ratio of the work out to the work in. What's the work in? The efficiency is 55% so, 55% of the work in is returned.

I'm having trouble understanding how to calculate the work in... :(

Also it says calculate the "rate", so how would the answer be expressed? J/s?

Edit: I've never posted this anywhere before.
 
  • #4
Flatshoe said:
I'm having trouble understanding how to calculate the work in... :(

Also it says calculate the "rate", so how would the answer be expressed? J/s?

Edit: I've never posted this anywhere before.

Work is Joules/s. 580 kg/s fall off the dam. So work in is the energy associated with the mass that falls each second. What's the energy associated with the mass?
 
  • #5
Squeezebox said:
Work is Joules/s. 580 kg/s fall off the dam. So work in is the energy associated with the mass that falls each second. What's the energy associated with the mass?
Kinetic energy? 1/2mv^2 = 1/2(580)(41.552)^2 = 500704 J = 500.704 KJ

Is that the right calculation for the work in?
 
  • #6
Flatshoe said:
Kinetic energy? 1/2mv^2 = 1/2(580)(41.552)^2 = 500704 J = 500.704 KJ

Is that the right calculation for the work in?

Yes, now how does that relate to work in and finally, work out.
 
  • #7
Squeezebox said:
Yes, now how does that relate to work in and finally, work out.

Thanks, I understand it now!
 

1. What is mechanical energy?

Mechanical energy is the energy that an object possesses due to its motion or position. It can be either kinetic energy, which is the energy of motion, or potential energy, which is the energy stored in an object's position or configuration.

2. How is mechanical energy related to efficiency?

Mechanical energy is related to efficiency because it is a measure of how well a mechanical system can convert energy from one form to another. A more efficient system will be able to convert a higher percentage of its input energy into useful mechanical energy output.

3. What factors affect the efficiency of a mechanical system?

The efficiency of a mechanical system can be affected by various factors, such as friction, mechanical losses, and design flaws. Additionally, the materials used, lubrication, and operating conditions can also impact the efficiency of a system.

4. How is mechanical efficiency calculated?

Mechanical efficiency is calculated by dividing the output mechanical energy by the input mechanical energy, and then multiplying by 100 to get a percentage. This can also be expressed as the ratio of useful work output to the total work input.

5. How can mechanical efficiency be improved?

Mechanical efficiency can be improved by reducing friction through the use of lubricants, optimizing the design and materials used in the system, and minimizing energy losses through proper maintenance and operation. Additionally, advanced technologies and materials can also help improve mechanical efficiency.

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