L6-Fall+2011

L6-Fall+2011 - MAE 14:650:474 Alternative Energy Systems...

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MAE 14:650:474 Alternative Energy Systems Lecture 6: Class Agenda o Hydro power 1
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MAE 14:650:474 Alternative Energy Systems Hydropower – hydraulic analysis o a qualitative analysis of a hydroelectric dam involved two components: s s 2 o a general arrangement of a hydraulic dam is presented s s B A dam turbine valves
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MAE 14:650:474 Alternative Energy Systems Hydropower – hydraulic analysis o hydraulic analysis starts with writing the conservation of energy from station A to station B (use Bernoulli’s principle) = + + + + + + = + + N n c t T n n n n n n B B B A A A g g W f C K D L f g V Z g V P Z g V P n 1 2 2 2 2 2 2 γ 3 s P = pressure, V=velocity, Z=elevation, γ =specific weight, f=friction factor, L=pipe length, D=diameter, K=minor loss, C=minor loss, f T =fully-rough friction factor, W t =change in head across the turbine, N=number of pipe segments, gc is used when the English engineering system is employed and is defined as: B A dam turbine valves 2 2 1 174 32 sec / sec / . - - - - = = N kg m lbf lbm ft c g
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MAE 14:650:474 Alternative Energy Systems Hydropower – hydraulic analysis o hydraulic analysis starts with writing the conservation of energy from station A to station B (use Bernoulli’s principle) = + + + + + + = + + N n c t T n n n n n n B B B A A A g g W f C K D L f g V Z g V P Z g V P n 1 2 2 2 2 2 2 γ 4 s The free surfaces of the water levels: A and B, upstream and downstream are at atmospheric pressure, thus P A = P B . s Since the velocities of the surfaces of the upstream and downstream reservoir are low, V A = V B . After substituting this into the above equation: s The change in head across the turbine is the difference in elevation minus the major and minor losses = + + - - = N n T n n n n n n B A c t n f C K D L f g V Z Z g g W 1 2 2
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MAE 14:650:474 Alternative Energy Systems Hydropower – hydraulic analysis o incorporating flow rate, Q: 5 o substituting this expression into the turbine head: o maximum flow rate (in the absence of a pump) occurs when the turbines extract no energy – change in head across the turbine is zero. Thus, the major and minor losses are equal to the elevation difference. o maximum change in head across the turbine occurs when the flow rate vanishes.
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MAE 14:650:474 Alternative Energy Systems Hydropower – hydraulic analysis o since the power extracted by a turbine is: o maximum flow rate and maximum change in head conditions result in
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L6-Fall+2011 - MAE 14:650:474 Alternative Energy Systems...

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