To study the flow of a liquied through a narrow tube, the following formula is used :` eta = (pi)/(8) (Pr^4)/(VI),` where letters have their usual meaning. The value of P, r, V and I are 76 cm of Hg col. `0.28 cm, 1.2 cm^3 s^(-1) and 18.2cm` respectively. If these quantities are measured to the accuracy of `0.1 cm of Hg col., 0.01 cm, 0.1 cm^3 s^(-1)` and 0.1 cm respectively, find the percentage error in the value of `eta.`

Explanation

To find the percentage error in the value of \( \eta \) using the formula:

\[ \eta = \frac{\pi}{8} \cdot \frac{P r^4}{V I} \]

we need to determine the contributions of the errors in the measurements of \( P \), \( r \), \( V \), and \( I \).

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