When liquid flows under pressure P through a tube of length l, the volume flow rate (ie. the volume per unit time), V, depends on the radius,r , of the tube, the pressure gradient (P/l) and the viscocity of the liquid.
Using the units cm, g and s
volume flow rate : dimension = cm^3/s
radius : dimension = cm
pressure gradient: g.cm/(s^2.cm)= g/s^2
viscosity (g.cm.s/s^2)/(cm^2) = g.cm/s
So according to the relationship, the equality in the dimensions become:
cm^3/s = (cm)^x * (g/s^2)^y * (g.cm/s)^z (x, y z unknown powers)
In order to cancel off the g, and have s at the bottom, choose y=1 and z=-1
Hence right side simplifies to (cm)^x * 1/s * (cm) ^-1
and for equality of dimensions x= 4
Form of the formula is
V = K (r^4)*(pressure gradient)/ viscosity where k is some constant
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