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 ∞ η ^{x} r^{y} (P/l)^{z}**

So, **V = K η ^{x} r^{y} (P/l)^{z} …. …. (1)**

Where k is a constant of proportionality. Rewriting the equation (1) in terms of dimensions,

[L^{3}T^{-1}] = [ML^{-1}T^{-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} r^{4} (P/l)^{1}**

**V = kPr ^{4}/η∫**

Experimentally k is found to be equal to π/8

So, **V = πPr ^{4 }/ 8η∫**

It is known as **Poiseuille’s equation.**