Oil is ?owing at a discharge of 0.50 m3=s in a 4-km, 50-mm-diameter steel pipe. The elastic modulus of the pipe is 200 · 106 kPa and its thickness is 5 mm. The oil has a speci?c gravity of 0.86 and a bulk modulus of 1.50 · 106 kPa. A valve at the end of the pipe is partially closed in a rapid fashion so that water hammer occurs anda pressure wave propagates upstream in the pipe.
The magnitude of the pressure wave is not to be greater than 600 kPa. Determine the percent decrease of ?ow rate tolerable during the valve closure and the period of the water hammer oscillation.