Applied Hydraulics #$3\mathrm{.}5\mathrm{.}15.$

A water supply pipeline contains a long segment that is horizontal and $30cm$ in diameter $($cast iron$).$ A leak along an inaccessible portion of the buried pipeline is highly likely. A pair of pressure gauges located upstream of the leak indicate a pressure drop of $23,000\frac{N}{m^2}.$ Another pair of pressure gauges located downstream of the leak indicate a pressure drop of $20,900\frac{N}{m^2}.$ The distance between the gages in each pair is $100m.$ Determine the magnitude of the leak. Assume that minor Iosses are negligible and that the water temperature is $20C.$