Oil with a specific gravity of S = 0.90 is flowing at 20 ft3 /sec through a 20-in.-diameter 13,000-ft-long pipe. The elastic modulus of the steel pipe is E =29 × 106 lb/in2 , its thickness is 0.40 in. and the bulk modulus of elasticity of the oil is B = 217,000 lb/in2 . A valve at the downstream end of the pipe is partially closed very rapidly so that a water hammer event is initiated and a pressure wave propagates upstream. If the magnitude of the wave is not to exceed 90 lb/in2 , determine:
(a) The percent decrease of flow rate tolerable during the valve closure.
(b) The time it takes the pressure wave to reach the upstream end of the pipe.