The question is incomplete. The complete question is :
The pressure difference, Δp, across a partial blockage in an artery (called a stenosis) is approximated by the equation :
Where V is the blood velocity, μ the blood viscosity {FT/L2}, ρ the blood density {M/L3}, D the artery diameter, the area of the unobstructed artery, and A1 the area of the stenosis. Determine the dimensions of the constants and . Would this equation be valid in any system of units?
Solution :
From the dimension homogeneity, we require :
Here, x means dimension of x. i.e.
So, dimensionless
So, and are dimensionless constants.
This equation will be working in any system of units. The constants and will be different for different system of units.