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

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Summary

This section introduces the comprehensive theory of compressible flow, covering isentropic, shock, and expansion phenomena together with frictional (Fanno) and heat-transfer (Rayleigh) effects in ducts and nozzles. Emphasis is placed on key parameters like the Mach number and the use of various analytical tools to predict how supersonic flows behave when subjected to geometric changes or environmental disturbances. The discussion extends to open-channel flow, where gravitational forces and channel geometry dominate. Together, these topics form a cornerstone in both high-speed aerodynamics and hydraulic engineering, providing engineers with the fundamental methods to analyze and design devices ranging from jet engines to water conveyance systems.

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Example Problems

Example 1

An ideal gas flows adiabatically through a duct. At section $1, p_{1}=140 \mathrm{kPa}, T_{1}=260^{\circ} \mathrm{C},$ and $V_{1}=75 \mathrm{m} / \mathrm{s},$ Farther downstream, $p_{2}=30 \mathrm{kPa}$ and $T_{2}=207^{\circ} \mathrm{C}$. Calculate $V_{2}$ in $\mathrm{m} / \mathrm{s}$ and $s_{2}-s_{1}$ in $\mathrm{J} /(\mathrm{kg} \cdot \mathrm{K})$ if the gas is $(a)$ air, $k=1.4$ and $(b)$ argon, $k=1.67$

Example 2

Solve Prob. P9.1 if the gas is steam. Use two approaches: (a) an ideal gas from Table $A .4$ and $(b)$ real gas data from the steam tables [15]

Example 3

If $8 \mathrm{kg}$ of oxygen in a closed tank at $200^{\circ} \mathrm{C}$ and $300 \mathrm{kPa}$ is heated until the pressure rises to $400 \mathrm{kPa}$, calculate $(a)$ the new temperature, ( $b$ ) the total heat transfer, and $(c)$ the change in entropy.

Example 4

Consider steady adiabatic airflow in a duct. At section B, the pressure is 600 kPa and the temperature is $177^{\circ} \mathrm{C}$. At section $\mathrm{D}$, the density is $1.13 \mathrm{kg} / \mathrm{m}^{3}$ and the temperature is $156^{\circ} \mathrm{C} . (a)$ Find the entropy change, if any. (b) Which way is the air flowing?

Example 5

Steam enters a nozzle at $377^{\circ} \mathrm{C}, 1.6 \mathrm{MPa}$, and a steady speed of $200 \mathrm{m} / \mathrm{s}$ and accelerates isentropically until it exits at saturation conditions. Estimate the exit velocity and temperature,