Book cover for Fundamentals of Fluid Mechanics

Fundamentals of Fluid Mechanics

Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein

ISBN #9781119080701

8th Edition

1,309 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter provides an in-depth exploration of turbomachines, detailing the fundamental energy and angular momentum principles that govern their operation. It examines the design and performance characteristics of centrifugal pumps, fans, and turbines, with particular emphasis on factors such as NPSH, pump-system matching, and the application of similarity laws via dimensionless parameters. Understanding these concepts enables engineers to predict and optimize machine performance in various fluid dynamics applications.

Learning Objectives

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Key Concepts

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Example Problems

Example 1

The rotor shown in Fig. $P 12.1$ rotates clockwise. Assume that the fluid enters in the radial direction and the relative velocity is tangent to the blades and remains constant across the entire rotor. Is the device a pump or a turbine? Explain.

Example 2

The measured shaft torque on the turbomachine shown in Fig. $P 12.2$ is $-60 \mathrm{N} \cdot \mathrm{m}$ when the absolute velocities are as indicated. Determine the mass flowrate. What is the angular velocity if the magnitude of the shaft power is $1803 \mathrm{N} \cdot \mathrm{m} / \mathrm{s} ?$ Is this machine a pump or a turbine? Explain.

Example 3

Uniform horizontal sheets of water of 3 -mm thickness issue from the slits on the rotating manifold shown in Fig. P12.3. The velocity relative to the arm is a constant $3 \mathrm{m} / \mathrm{s}$ along each slit. Determine the torque needed to hold the manifold stationary. What would the angular velocity of the manifold be if the resisting tcrque is negligible?

Example 4

At a given radial location, a 15 -mph wind against a vindmill (see Video $V 12.1$ ) results in the upstream ( 1 ) and downsream (2) velocity triangles shown in Fig. P12.4. Sketch an approsriate blade section at that radial location and determine the energy ransferred per unit mass of fluid.

Example 5

Sketch how you would arrange four 3 -in.-wide by 12 -in. long thin but rigid strips of shect metal on a hub to create a xindmill like the one shown in Video $V 12.1$. Discuss, with the help of velocity triangles, how you would arrange each blade on the hub and how you would orient your windmill in the wind.
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