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$[\overline{v'T'}] = \frac{1}{x_2 - x_1} \int_{x_1}^{x_2} v'T' dx$
%%should it be v't'?

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$\mathcal{H} = 2\pi a cos(\phi) \frac({c_p)(}{g)} \int_{0}^{p_s} [\overline{v'T'\;]  dp

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$R_o = \frac{u}{2\pi L}$,

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