The rate of a flow V a of liquid through a capillary under a constant pressure depends upon (i) the pressure gradient (P/l) (ii) coefficient of viscosity of the liquid eta (iii) the radius of the capillary tube r. Show dimesionally that the rate of volume of liquid flowing per sec V∝ Pr^4 /ηl

The rate of a flow V a of liquid through a capillary under a constant

1.	The rate of a flow V a of liquid through a capillary under a constant pressure depends upon (i) the pressure gradient (P/l) (ii) coefficient of viscosity of the liquid eta (iii) the radius of the capillary tube r. Show dimesionally that the rate of volume of liquid flowing per sec V∝ Pr^4 /ηl
Answer» Solution :`V=k(P//l)^(x)R^(y)eta^(z), [L^(3)T^(-1)]=[ML^(-1)T^(-2)//L]^(x)L^(y)[ML^(-1)T^(-1)]^(z)`. SIMPLIFYING `x=1, y=4 z=-1`.