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Homework Help: Maximum flow rates through water turbines given power and head.

  1. Jun 27, 2011 #1
    1. The problem statement, all variables and given/known data

    Calculate the maximum flow rates through the Francis and the Samson turbines under the conditions specified:

    Table 1 Characteristics of some American water turbines, 1849–97, on the basis of 30-inch (760 mm) wheel and 12-inch (300 mm) head
    Type | Maximum power output | Efficiency (%)
    Francis | 0.15 kW / 0.20 horsepower| 79.7 at full power / 55.0 at half power
    ‘Samson’ | 1.38 kW / 1.85 horsepower | 82.0 at full power / 75.6 at half power

    2. Relevant equations

    Power = turbine efficiency * density of water * acceleration due to gravity * head * flow rate


    Flow rate = Power / (turbine efficiency * density of water * acceleration due to gravity * head)

    3. The attempt at a solution

    Does anyone know if the efficiency in this equation should be given as a percentage or fraction? i.e. 79.7% or 0.797

    Francis example...

    Density of water = 1000kg/m^3
    Acc due to gravity = 9.81 m/s^2

    At full power:
    Flow rate = 150/(0.797*1000*9.81*0.3)=0.064m^3/s

    At half power:
    Flow rate= (150/2)/(0.55*1000*9.81*0.3)=0.046m^3/s

    However I have a feeling I'm missing a step. I'd be grateful for anyone who could take a look. :) Thanks.
    Last edited: Jun 27, 2011
  2. jcsd
  3. Jun 28, 2011 #2
    I think your method and arithmetic is OK.

    Check if you should add the radius of the wheel to the head.
  4. Jun 28, 2011 #3
    looks ok to me
  5. Jun 28, 2011 #4
    Ah that's a good suggestion. Looking at the context and previous questions of the textbook though I don't think I need to. Thanks. :)
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