begin{split} p_{i} & = p_{f} \\ mv & = (m - dm_{g})(v + dv) + dm_{g} (v - u) \\ mv & = mv + mdv - dm_{g} v - dm_{g} dv + dm_{g} v - dm_{g} u \\ mdv & = dm_{g} dv + dm_{g} u \ldotp \end{split}\] Consider high-temperature combustion, stability, and the principles of electric and chemical propulsion

newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)begin{split} \int_{v_{i}} Now, dm g and dv are each very small; thus, their product dm gdv is very, very small, much smaller than the other two terms in this expression. We neglect this term, therefore, and obtain: Describe the application of conservation of momentum when the mass changes with time, as well as the velocity Coherent, up-to-date chapter on electrical propulsion balancing fundamentals with practical aspects and applications

Separate chapters on liquid, solid, and hybrid propulsion systems and a new chapter on thrust chambers including the new aerospike nozzleSince all vectors are in the x-direction, we drop the vector notation. Applying conservation of momentum, we obtain This thoroughly revised ninth edition includes discussion and analysis of recent advances in the field, representing an authoritative reference for students and working engineers alike. In any engineering field, theory is only as useful as it is practical; this book emphasizes relevant real-world applications of fundamental concepts to link "thinking" and "doing". This book will help readers: