expressed in rev/s.4.A water turbine is to be designed to produce 27 MW when running at 93.7 rpm under a headof 16.5 m. A model turbine with an output of 37.5 kW is to be tested under dynamicallysimilar conditions with a head of 4.9 m. Calculate the model speed and scale ratio. Assuminga model efficiency of 88%, estimate the volume flow rate through the model. It is estimatedthat the force on the thrust bearing of the full-size machine will be 7.0 GN. For what thrustmust the model bearing be designed?

Answered: A water turbine is to be designed to…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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expressed in rev/s.
4.
A water turbine is to be designed to produce 27 MW when running at 93.7 rpm under a head
of 16.5 m. A model turbine with an output of 37.5 kW is to be tested under dynamically
similar conditions with a head of 4.9 m. Calculate the model speed and scale ratio. Assuming
a model efficiency of 88%, estimate the volume flow rate through the model. It is estimated
that the force on the thrust bearing of the full-size machine will be 7.0 GN. For what thrust
must the model bearing be designed?

Expert Solution

Step 1

Introduction

In order to solve this problem, we must first determine the model's speed, the scale ratio between the model and the prototype, and the volume flow rate through the model, by using the power coefficient and head coefficient, and then we will determine the thrust force on the model bearing by using the thrust force on the prototype bearing that has been specified.

Given data:

$\begin{array}{rcl} the power produce by turbine (P) & = & 27 MW \\ the runner speed (N) & = & 93.7 rpm \\ the head of the pump {(H)}_{p} & = & 16.5 m \\ the model turbine output (P) & = & 37.5 kW \\ the head of the model {(H)}_{m} & = & 4.9 m \\ the model efficiency (η) & = & 88 % \end{array}$

Find out:

The model speed and the scale ratio.

The volume flow rate through the model.

The thrust force on the model bearing.

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