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g A steel water pipe has an inner diameter of 12 in. and a wall thickness of 0.25 in. Determine the longitudinal and hoop stresses developed in the wall of the pipe at point B for the two cases below. Also, for each case draw the state of stress on a volume element located on the wall at point B. (a) The valve A is opened and the flowing water has a pressure of 200 psi. (b) The valve A is closed and the water pressure is 250 psi.

User Vito Huang
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1 Answer

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Answer:

a)
\mathbf{\sigma _ 1 = 4800 psi}


\mathbf{ \sigma _2 = 0}

b)
\mathbf{\sigma _ 1 = 6000 psi}


\mathbf{ \sigma _2 = 3000 psi}

Step-by-step explanation:

Given that:

diameter d = 12 in

thickness t = 0.25 in

the radius = d/2 = 12 / 2 = 6 in

r/t = 6/0.25 = 24

24 > 10

Using the thin wall cylinder formula;

The valve A is opened and the flowing water has a pressure P of 200 psi.

So;


\sigma_(hoop) = \sigma _ 1 = (Pd)/(2t)


\sigma_(long) = \sigma _2 = 0


\sigma _ 1 = (Pd)/(2t) \\ \\ \sigma _ 1 = (200(12))/(2(0.25))


\mathbf{\sigma _ 1 = 4800 psi}

b)The valve A is closed and the water pressure P is 250 psi.

where P = 250 psi


\sigma_(hoop) = \sigma _ 1 = (Pd)/(2t)


\sigma_(long) = \sigma _2 = (Pd)/(4t)


\sigma _ 1 = (Pd)/(2t) \\ \\ \sigma _ 1 = (250*(12))/(2(0.25))


\mathbf{\sigma _ 1 = 6000 psi}


\sigma _2 = (Pd)/(4t) \\ \\ \sigma _2 = (250(12))/(4(0.25))


\mathbf{ \sigma _2 = 3000 psi}

The free flow body diagram showing the state of stress on a volume element located on the wall at point B is attached in the diagram below

g A steel water pipe has an inner diameter of 12 in. and a wall thickness of 0.25 in-example-1
g A steel water pipe has an inner diameter of 12 in. and a wall thickness of 0.25 in-example-2
User Hyui
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