Physics

Problem

Oceanographers sometimes write the total pressure at a point in moving sea-water as

P = P_0 + \rho g h + \tfrac12 \rho v^{2} + k \eta,

where

P_0

is reference pressure,

\rho

is water density,

g

is acceleration due to gravity,

h

is depth,

v

is the local speed of the current,

\eta

is the dynamic viscosity of water and

k

is a constant. a. (a) Find the dimensions of

k

so that the last term has the same dimensions as pressure. b. (b) Hence comment whether the given expression is dimensionally homogeneous in its present form.

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