a Consider a submarine of total mass m = 1250 metric tons (1 metric ton = 10²kg) and whose structure can be crudely mode

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A Consider A Submarine Of Total Mass M 1250 Metric Tons 1 Metric Ton 10 Kg And Whose Structure Can Be Crudely Mode 1 (523.27 KiB) Viewed 12 times

a Consider a submarine of total mass m = 1250 metric tons (1 metric ton = 10²kg) and whose structure can be crudely modelled as a cylinder (radius R, length L) closed by two hemispheres (radius R). By either filling or emptying its ballast of sea water, the submarine can dive or surface. This submarine is now cruising, being fully immersed in still waters (no current), and moving in a rectilinear, horizontal fashion at a constant speed U. In these (non-pitched) cruise conditions, the submarine exhibits a lift coefficient that is nil (Cų = 0.0) and a drag coefficient of Cp = 0.012 (with C_ and Cp based on the projected cross-sectional area of the submarine cylindrical envelope, as seen from the front). Let us assume that the flow field around the submarine, once projected in its vertical / symmetry plane, can be modelled as a potential flow around a 2D Rankine oval, of velocity potential given by: V (2 + In the above, U is the (relative) speed of the upstream flow, o stands for the strength of the doublet's source and sink, which are respectively located at (-x0,0,0) and (+X0,0,0) when expressed in the Cartesian reference frame [0, x, y, z) attached to the submarine (with x the axial coordinate pointing towards the submarine tail – see Fig. below) $ = Ux + 2x [in (J(x + xo)2 + y2) – In (J(x – xo)? + y2 + 22)] 2л у L/2 -X0 xo rine stays 1) Determine the corresponding 2D velocity field V = (u, v) and associated stagnation point(s) 2) Considering that the source/sink strength and x-coordinates are such that o = (91/4)RU and |xo| = 4R, infer what should be the length (L) of the submarine (as a function of R) 3) Evaluate by w many percent its overall vol me must be filled with water for the sub in static equilibrium conditions, with no inherent tendency to dive or surface. For this question, consider R = 5m. 4) Evaluate the hydrodynamic drag to be overcome by the propellers. For this question, consider R = 5m and U = 10 knots (1 knot = 1.85 km/h)