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FreeloaderUK wrote:

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in ww2 a submarine could achieve around 20knots surfaced, 8knots submerged.

modern SSKs usually around 12knots surfaced, 20knots submerged

SSNs usually around 18knots surfaced, over 25knots submerged

obviously variations are wide.

but what i want to know is- how come subs are slower on the surface than dived? in the past it was the other way round

Because, with a few exceptions, pre-ww2 submarines were optimized for surface, not submerged performance: they had long, narrow hulls to reduce wave-making resistance, and tons of drag-inducing crud above their surfaced waterline. Post-ww2, especially post-Albacore, submarines were optimized for submerged performance: they got rid of all the draggy (and noisy) cruft, like guns, optimized the hulls for reduced submerged drag (there's a reason modern submarines look a lot like blimps: the fluid dynamics are very similar), and accepted much higher levels of drag due to wave action on the surface.

seasick wrote:

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Slightly on a tangent:

Water is much heavier and denser than air but has no shear strength. But does have tensile strength hence the crush depth for submarines. The terminal velocity of an object moving through the air also applies to an object moving through water. The tear drop hull minimizes friction with the water and gives the water the best possible surface to flow over while the submarine pushes through the water. I am under the impression that since water and air are both mechanically considered fluids and that formulas used for determining drag and other such properties of a object moving through the air can be used with some modification for objects moving through water.

Water and air are both Newtonian fluids, so that the differential equations for most flow regimes are identical. In both cases, there is no tensile strength, and the only resistance to shearing forces from viscosity and the change in velocity in the direction normal to the local surface. The differences in behavior start when air can't be treated as a incompressible fluid (usually this is at freestream Mach numbers greater than about 0.5) or where water begins to exhibit cavitation.

The other category of fluids are non-Newtonian, a group which includes things like toothpaste, paint, and a correctly proportioned mix of cornstarch and water. It also includes many oils, especially those used for traction drives.