Two capillary tubes of equal length and inner radii 2r and 4r respectively are added in series and a liquid flows through it. If the pressure difference between the ends of the whole system is 8.5 cm of mercury, find the pressure difference between the ends of the first capillary tube.

Explanation

To solve the problem, we need to find the pressure difference between the ends of the first capillary tube when two capillary tubes of different radii are connected in series.

### Step-by-Step Solution:

1. **Understand the System**: We have two capillary tubes of equal length, with inner radii \( r_1 = 2r \) and \( r_2 = 4r \), connected in series. The total pressure difference across the entire system is given as \( \Delta P_{total} = 8.5 \, \text{cm of mercury} \).

2. **Use Poiseuille’s Law**: The pressure drop across a capillary tube due to viscous flow can be described by Poiseuille’s Law:
\[
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