A 700-m-long, 2.0-m-diameter steel penstock conveys water from a reservoir to a turbine. The reservoir water surface is 150 m above the turbine, and the flow rate is 77.9 m3/sec. Agate valve is installed at the downstream end of the pipe. Determine the wall thickness to avoid damage to the pipeline if the gate valve is closed rapidly. Use this equation T(PD = 2T e) to determine the allowable pressure the pipe can withstand based on hoop stress theory with T = 1.1 × 108 N/m2. Neglect longitudinal stresses and assume that the operational pressure is minimal compared to the maximum water hammer pressure.
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