A Venturi meter in a water main has a pipe area of $50\ \text{cm}^2$ and a throat area of $10\ \text{cm}^2$. Its mercury manometer shows a difference of $4.0\ \text{cm}$. What volume of water flows each second? (Mercury $13\,600\ \text{kg/m}^3$, $g = 9.8\ \text{m/s}^2$.)