Question

To calculate the maximum allowable stresses in pressure vessels, compute the minimum allowable thickness of pressure vessels to meet certain constraints, and observe and compare properties of different pressure vessel shapes.

Engineers are considering two possible vessel shapes for storing fuel. One shape is cylindrical and the other is spherical. Each vessel would be constructed out of the same material such that its hoop stresses and longitudinal stresses would be no greater than 20.0 ksi . The cylindrical pressure vessel has an inside diameter of dc = 29.0 in and a thickness of tc = 0.500 in . The spherical pressure vessel has an inside diameter of ds = 27.0 in and a thickness of ts = 0.250 in .

A: Determine the maximum allowable pressure, pc,max, in the cylindrical pressure vessel.

B: Determine the maximum allowable pressure, ps,max, in the spherical pressure vessel.

C: Determine the required thickness of the cylindrical pressure vessel, tr, if it is subjected to the maximum allowable pressure of the spherical pressure vessel that was calculated in Part B.

Answer 1

A) p_max = 0.69 ksi .... Hoop design constraint

B) p_max = 0.37 ksi .... Hoop design constraint

C) tr_max = 0.26825 in .... Hoop design constraint

Step-by-step explanation:

Given:-

- The inside diameter of cylindrical vessel, dic = 29.0 in

- The thickness of cylindrical vessel, tc = 0.5 in

- The maximum hoop and longitudinal stresses, σmax = 20.0 ksi

- The inside diameter of spherical vessel, dis = 27.0 in

- The thickness of spherical vessel, ts = 0.25 in

Solution:-

- The relations for Hoop (σh) and Longitudinal (σl) stresses in thin-walled vessels are:

σh = p*di / 2*t

σl = p*di / 4*t

A)

The pressure allowed as per Hoop Stress constraint:

σh = p*dic / 2*tc

p = 2*σmax*tc / dic

p = 2*(20)*(0.5) / 29 = 0.68965 kips

The pressure allowed as per Longitudinal Stress constraint:

σl = p*dic / 4*tc

p = 4*σmax*tc / dic

p = 4*(20)*(0.5) / 29 = 1.37931 kips

- The maximum allowable pressure for the cylindrical vessel would be:

p_max,c = min ( 0.68965 , 1.37931 )

p_max,c = 0.69 kips .... Hoop design constraint

B)

The pressure allowed as per Hoop Stress constraint:

σh = p*dis / 2*ts

p = 2*σmax*ts / dis

p = 2*(20)*(0.25) / 27 = 0.37037 kips

The pressure allowed as per Longitudinal Stress constraint:

σl = p*dis / 4*ts

p = 4*σmax*ts / dis

p = 4*(20)*(0.25) / 27 = 0.74074 kips

- The maximum allowable pressure for the cylindrical vessel would be:

p_max,s = min ( 0.37037 , 0.74074 )

p_max,s = 0.37 kips .... Hoop design constraint

C)

The thickness required as per Hoop Stress constraint:

σh = p_max,s*dic / 2*tr

tr = p_max,s*dic / 2*σh

tr = 0.37*29 / 2*20 = 0.26825 in

The thickness required as per Longitudinal Stress constraint:

σl = p_max,s*dic / 4*tr

tr = p_max,s*dic / 4*σh

tr = 0.37*29 / 2*20 = 0.13413 in

- The thickness required for the cylindrical vessel would be:

tr_max = max ( 0.26825 , 0.13413 )

tr_max = 0.26825 in .... Hoop design constraint

Answer 2

The answer and explanation are attached