Answer to Question #126599 in Mechanical Engineering for Dorado

Question

(c) In order to avoid excessively high stress in the pipeline during valve closure, it is proposed that the time to fully close the valve is not shorter than 15 s. Is this a safe closure time given that the maximum allowable hoop stress in the pipe is 110 MPa? Use a steady discharge of 15 m3 /s if you were not successful with part (a). (Aide mem: hoop stress, σH= pd/2t , where p,d,t are pipe pressure, diameter and wall thickness respectively.)

Answer 1

steady discharge= $15 \frac{ m^3}{s}$ , maximum allowable hoop stress = 110 MPa ,

Net flow of water in 15 s= $15\times 15 =225 m^3$

maximum stress due to that water

$\sigma_h=\frac {Pd}{2t}= \frac{1000\times 10\times d^2}{2t}$

$\sigma _h = \frac{1000\times 10 \times3 \times flow}{2\times 15\times 3.14\times 4}$

$\sigma _h=17914$ pa

$\sigma_h= 17.914 MPa$

so it will be safe