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### Topic: Friction Loss in Turbine Water Power System  (Read 13805 times)

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#### Dolphinsiu

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##### Friction Loss in Turbine Water Power System
« on: September 18, 2007, 04:52:21 AM »
I meet one question that is very difficult although the answer is given!

Q. Water is stored in an elevated reservoir. To generate power, water flows from this reservoir down through a large conduit to a turbine and then through a similar-sized conduit. At a point in the conduit 89.5 m above the turbine, the pressure is 172.4 kPa, ans at a level 5 m below the turbine, the pressure is 89.6 kPa. The water flow rate is 0.800 m3/s. The output of the shaft of the turbine is 658 kW.The water density is 1000 kg/m3. If the efficiency of the turbine in converting the mechanical energy given up by the fluid to the turbine shaft is 89% (nt = 0.89), calculate the friction loss in the turbine in J/kg. Note that in the mechanical-energy balance equation, is equal to the output of the shaft of the turbine over nt.                         Ans. F = 85.3 J/kg

By Mechanical-energy balance equation,

(p2 - p1)/ρ + 1/2 (u2^2 - u1^2) + g(z2 - z1) - F = ntWp
-82.8 + 0 + 9.8 (5 - 89.5) - F = - 0.89 (658 x 10^3) / (1000 x 0.8 )
F = - 178.9 J/kg

What's wrong with my calculation?? Why it is equal to 85.3 J/kg in text book answer?
« Last Edit: September 28, 2007, 01:05:34 PM by Dolphinsiu »

#### Donaldson Tan

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##### Re: Friction Loss in Turbine Water Power System
« Reply #1 on: September 23, 2007, 10:48:20 AM »
Your application of the equation is wrong.

Energy Transferred to Turbine = Difference in Mechanical Energy of Water.

Since the turbine is 89% efficient, then 11% of the energy transferred to the turbine must be consumed by friction, thus:

F = (1 - nt)(p2 - p1 + 0.5ρ(u22 - u12) + g(z2- z1))
"Say you're in a [chemical] plant and there's a snake on the floor. What are you going to do? Call a consultant? Get a meeting together to talk about which color is the snake? Employees should do one thing: walk over there and you step on the friggin� snake." - Jean-Pierre Garnier, CEO of Glaxosmithkline, June 2006

#### Dolphinsiu

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##### Re: Friction Loss in Turbine Water Power System
« Reply #2 on: September 28, 2007, 01:06:53 PM »
Sorry! I haven't typed the bold word in last time. Will I still apply it correctly?

#### BenH

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##### Re: Friction Loss in Turbine Water Power System
« Reply #3 on: January 19, 2011, 11:40:57 AM »
I know this is an old post, but I just encountered myself with this problem also. I think the balance you are considering must include the n (efficency) dividing the total work.

On the other hand, you should consider the distance 1 = -89.5 m, since it is above the turbine.

Does this makes sense to anyone?