Question

13. (a) The cylindrical walls of a vessel of outer radius R and wall thickness (t <<R) are made of an isotropic linear elastic material with modulus E and Poisson's ratio v. The end caps are rigid. If the vessel is empty (zero gage pressure), the vessel fits precisely (without any stress) inside a rigid frictionless well. A pressurized fuel is introduced in the vessel so that the internal gage pressure in the vessel is now P. For these conditions in the cylindrical walls of the vessel which of the following is/are true? No change in outer radius and therefore zero radial strain. PR On = t L = PR /2t (iv) En = - VEL Oh = VOL (b) The walls of a cylindrical pressure vessel of radius R = 1 m, and wall thickness t = 2 cm are made of an isotropic linear elastic material with modulus E = 10.0 GPa, Poisson's ratio v = 0.2, and coefficient of thermal expansion a = 1 x 10 °C. When a hot fluid at pressure p is introduced in the vessel, the temperature of the wall increases by AT = 100 °C, and the radius of the vessel increases by dr = 1 mm. Find the value of the pressure p.

Answer 1

@ HAS when the pressure applied on this foi vessel the radius of the cylindes will changes so that option option liligo 62. oong for this linders 66- PR option hi GL = PR cylis so 2 is true t true at in] En: -VEL we know that for this Sylieder En PD (-2-12 4t EL= PD (1-21) THE En '2-11 1-21 2014 En EL 2-ll 1-2 l EL is wmony Optima in 66=264 os 66=Q6L Gh= PR 6u = PR t 2+ : - is won : opsion (0) song Seanned with CamScanner

2 @ Givens Rolm - d: 2m t=2cm = 2X10 m E 10 G Paz 10x63 mpe = 20mm 2=146 /ec 1=0.2 AT=100c fona, Shalom - Sp: 20m Eh=8d - P.D (2-1). d 4tE Px 20000 2 2000 (2-0.2] 3 4x20x 10 x 10 = 0.222 MPa Pressure Pressusedue to change in this we Roow that 6. E. L.AT - COX 603 x 186 x 100 = 6 ima CamScanner

we 1200w that perisaum Stress aceurs on thin. pressure vessule is :.6 hP.D Hoop Streps 27 1x 2 x 0 zero Pressure P. 0.02 mla :. Total Press on Cylinders: ¿ 0.22+0.2 -0.24 mPa. P=0.24 MPa lics Scarved with CamScanner

A)

1) Falls 2) true 3)True 4)Falls 5) Falls

B) Pressure = 0.24 MPa