Question

Problem 4. A water reservoir is open at the top, and has radius r 50 ft and wall thickness t 10 in. what height h of the water will produce a circumferential (hoop) stress of 700 psi in the wall of the reservoir? What is the longitudinal (i.e. axial) stress in the wall due to the water? HINT: Water has a weight density of 62 lb/ft3 (so the pressure is caused by the weight of water), and the reservoir is sitting on the ground! Assume the reservoir container itself is weightless

Answer 1

r = 50 ft or dia = 100 ft = 1200 inch thickness (t) = 10 inch. Q_R = 700 psi = (700 times 12 times 12) psft P = rho gh = 62 times 32.2 times h = 1996.4 h lb/ft^2 where h is in ft. Q_R = pd/2t = 1996.4 times h times 1200/2 times 10 h = (700 times 12 times 12/60 times 1996.4) ft. h = 0.8415 ft Since, the reservoir is sitting on the ground, the longitudinal stress in the wall will be 0(zero).