Fluid Mechanics

Frank M. White

ISBN #9789385965494

8th Edition

1,418 Questions

24,047 Students Helped

Homework Questions

Summary

Learning Objectives

Key Concepts

Example Problems

Explanations

Common Mistakes

Summary

Compressible flow differs significantly from incompressible flow primarily through variations in density and the influence of thermodynamic effects. The Mach number is the key parameter that distinguishes flow regimes and governs phenomena such as choking and shock wave formation. Understanding these effects is critical for the design and analysis of high-speed applications, including supersonic airfoils, rocket nozzles, and gas pipelines. Modern computational tools have greatly enhanced our ability to analyze these complex phenomena, but engineers must be cautious about assumptions and boundary conditions.

Learning Objectives

Key Concepts

CONCEPT

DEFINITION

No concepts available

No definitions available for this book.

Example Problems

Example 1

Prove that the streamlines $\psi(r, \theta)$ in polar coordinates from Eqs. (8.10) are orthogonal to the potential lines $\phi(r, \theta)$.

Example 2

The steady plane flow in Fig. $\mathrm{P} 8.2$ has the polar velocity components $v_{\theta}=\Omega r$ and $v_{r}=0 .$ Determine the circulation $\Gamma$ around the path shown.

Example 3

Using cartesian coordinates, show that each velocity component $(u, v, w)$ of a potential flow satisfies Laplace's equation separately.

Example 4

Is the function $1 / r$ a legitimate velocity potential in plane polar coordinates? If so, what is the associated stream func$\operatorname{tion} \psi(r, \theta) ?$

Example 5

A proposed harmonic function $F(x, y, z)$ is given by \[ F=2 x^{2}+y^{3}-4 x z+f(y) \] (a) If possible, find a function $f(y)$ for which the laplacian of $F$ is zero. If you do indeed solve part $(a),$ can your final function $F$ serve as $(b)$ a velocity potential or $(c)$ a stream function?