Maximum flow rates through water turbines given power and head.

[PhysicsStudy]

Homework Statement

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

Homework Equations

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

so

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

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.

 

[edgepflow]

I think your method and arithmetic is OK.

Check if you should add the radius of the wheel to the head.

 

[W R-P]

looks ok to me

 

[PhysicsStudy]

I think your method and arithmetic is OK.

Check if you should add the radius of the wheel to the head.

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. :)