ensure streaming flow of the given liquid thought the capillary tube and determine the coefficent of viscosity of the same using poiseuille's methord(ro= 1000kg/m3, g=9.8m/s)
Answers
Poiseuille 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 land 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 η, r and the pressure gradient p/l.
(i.e) V α ηx r y (P /l)z
V=k ηx r y (P /l)z
where k is a constant of proportionality. Rewriting equation (1) in terms of dimensions,
[L3T-1] = [ML-1 T-1] x [L]y[ML-1T-2 / L]z
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= kPr4/ ηl
Experimentally k was found to be equal to π/ 8
V = πPr4 / 8 ηl