Check the accuracy of the relation `eta= (pi)/(8)(Pr^4)/(lV)`
Here, P is pressure, V= rate of flow of liquid through a pipe, `eta` is coefficient of viscosity of liquid.

Explanation

To check the accuracy of the relation \( \eta = \frac{\pi}{8} \frac{P r^4}{l V} \), we will use dimensional analysis. Here, \( P \) is pressure, \( V \) is the rate of flow of liquid through a pipe, \( \eta \) is the coefficient of viscosity, \( r \) is the radius of the pipe, and \( l \) is the length of the pipe.

### Step 1: Identify the dimensions of each quantity involved.

1. **Coefficient of Viscosity (\( \eta \))**:
- The coefficient of viscosity can be defined as shear force per unit area per unit velocity gradient.
- Its dimensions can be derived as:
\[
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