Dimensional Analysis homogeneous

[Larrytsai]

Determine which of the following equations are dimensionally homogeneous. Show
your work
ΔP/Q = 17L(μ)/(w^4)


where ΔP is the pressure drop in a channel of triangular cross-section, Q is the
volumetric flowrate, L is the channel length, μ is the fluid viscosity, and 2w is the
length of one side of the trianglei have

ΔP = F/A = ML(T^-2)
Q = volume/seconds = (L^3)/T

so...

ΔP/Q = M(T^-1)(L^-4)

For the other side of the equation I do not know how to deal with fluid viscosity and do I ignore the 17?

 

[lewando]

The viscosity, μ, has units of Pa⋅s, or (N⋅s)/m², or kg/(m⋅s). Yes, ignore the unitless constant 17.

ΔP = F/A = ML(T^-2)

does not look right.

 

[Larrytsai]

Thank you so much I have spotted the problem