Dimensions of physical quantities

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Question

The rate of flow (V) of a liquid (coefficient of viscosity is $η$ ) flowing through a pipe of radius r , length L and pressure gradient p is given by Poiseuille's equation $V = \frac{π}{8} \frac{r^{x}}{η^{z} L} p^{y}$ . Then calculate the value of x.

Moderate

Solution

Since we know that $V = \frac{π}{8} \frac{r^{4}}{ηL} p$ , so we get x = 4, y = 1 and z = 1.

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