Poiseuillie investigated the steady flow of a liquid through a capillary tube. He derived an expression for the volume of the liquid flowing per second through the tube.
Consider a liquid of co-efficient of viscosity η flowing, steadily through a horizontal capillary tube of length / and radius r. If P is the pressure difference across the ends of the tube, then the volume V of the liquid flowing per second through the tube depends on n. r and the pressure gradient (P/∫).
But, V ∞ ηx ry (P/l)z
So, V = K ηx ry (P/l)z …. …. (1)
Where k is a constant of proportionality. Rewriting the equation (1) in terms of dimensions,
[L3T-1] = [ML-1T-1]x
Equating the powers of L. M and T on both sides we get x = -1, y = 4 and z= 1
Substituting in equation (1),
V = K η-1 r4 (P/l)1
V = kPr4/η∫
Experimentally k is found to be equal to π/8
So, V = πPr4 / 8η∫
It is known as Poiseuille’s equation.
