Fluid Machinery Turbine Radial Flow

[Dibbs]

Homework Statement

The speed of a radial-flow reaction water turbine operating under BEP conditions is 1200 rpm. The diameter of the turbine runner is 0.25 m, the inlet angle and width of the runner vanes are 125° and 70mm respectively, and the inlet guide-vane anle is 25°. The hydraulic and overall efficiencies of the turbine are 86.5% and 81% respectively. Neglecting the thickness of the runner vanes determine the net turbine head, the turbine discharge, the turbine brake power

Homework Equations

Tω/γQH = η (overall)
Hm/H = η (mech)
Q=AV
u=rω

The Attempt at a Solution

Given N=1200 rpm we can find tangential velocity of runner u = rω=15.71 m/s
Since we know the inlet guide angle 25°, the angle of runner vane 125°, and u and we can draw triangle to represent the fluid relative, absolute and radial velocities and thus calculate the radial velocity. Using Q =AV we can determine Q the turbine discharge. For BEP we can can determine H as we know runner diameter D and speed n and can obtain phi at BEP from charts. For turbine brake power =γQHm and Hm can be found since we know H

Not sure of this approach as the question did not refer to the efficeincy vs specific speed chart where I estimated phi from. Also solving the triangle in that way seems a bit dodgy.
Would love to hear of any other approach to this
Thank you

statement, all variables and given/known data[/b]

Homework Equations

The Attempt at a Solution

 

[Valkarie]

Given N=1200 rpm we can find tangential velocity of runner u = rω= 15.71 m/sSince we know the inlet guide angle 25°, the angle of runner vane 125°, and u and we can draw triangle to represent the fluid relative, absolute and radial velocities and thus calculate the radial velocity. Using Q =AV we can determine Q the turbine discharge. For BEP we can can determine H as we know runner diameter D and speed n and can obtain phi at BEP from charts. For turbine brake power =γQHm and Hm can be found since we know HTo determine the net turbine head, we can use the equation = (η mech) x Hmwhere η mech is the hydraulic efficiency, and Hm is the mechanical head. The turbine discharge, Q, can be found using the equationQ = AVwhere A is the area of the turbine runner, and V is the velocity of the water flow through the turbine. The turbine brake power can be calculated using the equationTBP = γQHmwhere γ is the specific weight of the water, Q is the turbine discharge, and Hm is the mechanical head.