(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

where the boldface type denotes a vector quantity. In general, the incremental surface dS may be expressed as r dψ R d∅. Examining Figure 1, we see that dS = R^{2}sin∅ dψ d∅ for this particular nozzle. Substituting Equations 3 and 4 in Equation 2 and integrating ∅ from zero to θ and ψ circumferentially from zero to π, we arrive at the result

2. Relevant equations

3. The attempt at a solution

When I integrate to get 5, I get 0.5ρv_{e}^{2}R^{2}sin^{2}θ instead. Shouldn't there be a 0.5 when you integrate sinθcosθ or did the paper miss out on something?

Source: https://mdao.grc.nasa.gov/publications/NASA-TM-105176-Diverge.pdf

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# Divergent nozzle

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