Derive an expression for the rate of flow of a liquid through a capillary tube. Assume that the rate of flow depends on i) pressure gradient `(P/l)` , (ii) The radius, r and (iii) the coefficient of viscosity , `eta` . The value of the proportionally constant k`=pi/8`

Explanation

To derive the expression for the rate of flow of a liquid through a capillary tube, we will follow these steps:

### Step 1: Understand the relationship
We start by stating that the rate of flow \( V \) of a liquid through a capillary tube is directly proportional to the pressure gradient \( \frac{P}{L} \), the radius \( r \) of the tube, and inversely proportional to the coefficient of viscosity \( \eta \). This can be expressed as:

\[ V \propto \frac{P}{L} \cdot r^A \cdot \eta^{-B} \]
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