Classes: Arachnida, Insecta (including Sub-Classes M y riapoda, Hexapoda), Crustacea (including Sub-Classes Entomostraca, Malacostraca), Epizoa (Epizootic Crustacea), Annellata (Chaeto p ods and Leeches), Cirripedia.
Generally if S denotes any closed surface, fixed in the fluid, M the mass of the fluid inside it at any time t, and 0 the angle which the outward-drawn normal makes with the velocity q at that point, dM/dt = rate of increase of fluid inside the surface, (I) =flux across the surface into the interior _ - f f pq cos OdS, the integral equation of continuity.
Taking the fixed direction parallel to the axis of x, the time-rate of increase of momentum, due to the fluid which crosses the surface, is - f'fpuq cos OdS = - f f (lpu 2 -+mpuv+npuw)dS, (1) which by Green's transformation is (d(uiu 2) dy dz dxdydz.
Then the quantity E cos OdS is the product of the normal component of the force and an element of the surface, and if this is summed up all over the surface we have the total electric flux or induction through the surface, or the surface integral of the normal force mathematically expressed by JE cos OdS, provided that the dielectric constant of the medium is unity.
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