Nomenclature

Dimensional quantities	Non-dimensional quantities	Description
L		half (axial) length of the solid block
P		pressure
μ		fluid viscosity
Φ		material modulus of rigidity
U	U* = μU / rFN	sliding velocity of the bottom surface
Q		volume flow rate
x∈[−L, L]	w∈[0,1]	axial coordinate (w defined separately on each segment
d ≡ d(x), d0	D = d / δ, D0	channel height, minimum channel height
δ		variation in channel height, max(d) – min(d)
r = δ / 2L		surface “roughness”
ξ		degree of surface asymmetry
FN	fN = FN / 6μU	net normal force
FT	fT = FT / 6μU	net tangential force (on bottom surface)