Book cover for Fluid Mechanics

Fluid Mechanics

Frank M. White

ISBN #9789385965494

8th Edition

1,418 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This section covers the fundamental concepts of pressure distribution in fluids, starting with hydrostatics and moving through practical applications such as manometers, buoyancy, and stability of floating bodies. Key derivations include the linear variation of pressure with depth in an incompressible fluid and modifications for layered fluids and rigid-body acceleration or rotation. The principles outlined form the foundation for more advanced analysis techniques such as control volume methods introduced later, and emphasize the importance of correct sign conventions, integration of pressure distributions over complex surfaces, and careful matching of theoretical models with practical measurement devices.

Learning Objectives

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Key Concepts

CONCEPT

DEFINITION

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Example Problems

Example 1

For the two-dimensional stress field shown in Fig. P2.1 it is found that $$\sigma_{x x}=3000 \mathrm{lbf} / \mathrm{ft}^{2} \quad \sigma_{y y}=2000 \mathrm{lbf} / \mathrm{ft}^{2} \quad \sigma_{x y}=500 \mathrm{lbf} / \mathrm{ft}^{2}$$ Find the shear and normal stresses (in $\operatorname{lbf} / \mathrm{ft}^{2}$ ) acting on plane $A A$ cutting through the element at a $30^{\circ}$ angle as shown.

Example 2

For the two-dimensional stress field shown in Fig. P2.1 suppose that $\sigma_{x x}=2000 \operatorname{lbf} / \mathrm{ft}^{2} \sigma_{y y}=3000 \operatorname{lbf} / \mathrm{ft}^{2} \sigma_{n}(A A)=2500 \mathrm{lbf} / \mathrm{ft}^{2}$ Compute $(a)$ the shear stress $\sigma_{x y}$ and $(b)$ the shear stress on plane $A A$

Example 3

A vertical, clean, glass piezometer tube has an inside diameter of $1 \mathrm{mm}$. When pressure is applied, water at $20^{\circ} \mathrm{C}$ rises into the tube to a height of $25 \mathrm{cm} .$ After correcting for surface tension, estimate the applied pressure in Pa.

Example 4

Pressure gages, such as the bourdon gage in Fig. P2.4, are calibrated with a deadweight piston. If the bourdon gage is designed to rotate the pointer 10 degrees for every 2 psig of internal pressure, how many degrees does the pointer rotate if the piston and weight together total 44 newtons?

Example 5

Quito, Ecuador, has an average altitude of $9350 \mathrm{ft}$. On a standard day, pressure gage A in a laboratory experiment reads $63 \mathrm{kPa}$ and gage $\mathrm{B}$ reads $105 \mathrm{kPa}$. Express these readings in gage pressure or vacuum pressure, whichever is appropriate.

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Step-by-Step Explanations

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Common Mistakes

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