The pressure difference, , across a partial blockage in an artery (called a stenosis) is approximated by the equation where is the blood velocity, the blood viscosity , the blood density , the artery diameter, the area of the unobstructed artery, and the area of the stenosis. Determine the dimensions of the constants and . Would this equation be valid in any system of units

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.

and 1and 1

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