Monday, 16 September 2019

EXAMPLE 1.4.3. HOOP STRESS

A large pipe called a penstock in hydraulic work is 1.5m in diameter. It is composed of wooden staves bound together by steel hoops, each  in cross-sectional area, and is used to conduct water from a reservoir to a powerhouse. If the maximum tensile stress permitted in the hoops is 130MPa, what is the maximum spacing between hoops under a head of water of 30m? (Use mass density of water = .


For one hoop, the FBD shows two F for the hoop against the hydrostatic force caused by pressure.



And the force of the hoops is computed as:





From the FBD, use statics to attain equilibrium (prevent the staves to explode).







where pressure,




So, the required length becomes:



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