Oceanographers sometimes write the total pressure at a point in moving sea-water as P…
PHYSICS · Multi-part · CBSE · Physics · Units and Measurements · Units and Measurements
Problem
Oceanographers sometimes write the total pressure at a point in moving sea-water as
P=P0+ρgh+21ρv2+kη,
where P0 is reference pressure, ρ is water density, g is acceleration due to gravity, h is depth, v is the local speed of the current, η is the dynamic viscosity of water and k is a constant.
(a) Find the dimensions of k so that the last term has the same dimensions as pressure.
(b) Hence comment whether the given expression is dimensionally homogeneous in its present form.