A small flat panel on a submarine hull is at a depth where the surrounding water is…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids

Invariance, Ch Index notation and Cartesian tensors

Problem

A small flat panel on a submarine hull is at a depth where the surrounding water is at rest and exerts an isotropic pressure

p = 2.5\,\mathrm{MPa}

on it, so the water's stress is

\sigma_{ij} = -p\,\delta_{ij}

. The panel's outward unit normal (pointing into the water) is

n_i = (0.6, 0, 0.8)

. ((a)) Write the traction on the panel,

t_i = \sigma_{ij}n_j

, in terms of

p

and

n_i

alone, carrying out the sum over

j

. ((b)) Evaluate the three components of

\mathbf{t}

and its magnitude.

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