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NNADVOKAT [17]
3 years ago
15

A spherical gas container made of steel has a(n) 17-ft outer diameter and a wall thickness of 0.375 in. Knowing that the interna

l pressure is 60 psi, determine the maximum normal stress and the maximum shearing stress in the container.
Engineering
1 answer:
Arte-miy333 [17]3 years ago
7 0

Answer:

Maximum Normal Stress σ = 8.16 Ksi

Maximum Shearing Stress τ = 4.08 Ksi

Explanation:

Outer diameter of spherical container D = 17 ft

Convert feet to inches D = 17 x 12 in = 204 inches

Wall thickness t = 0.375 in

Internal Pressure P = 60 Psi

Maximum Normal Stress σ = PD / 4t

σ = PD / 4t

σ = (60 psi x 204 in) / (4 x 0.375 in)

σ = 12,240 / 1.5

σ = 8,160 P/in

σ = 8.16 Ksi

Maximum Shearing Stress τ = PD / 8t

τ = PD / 8t

τ = (60 psi x 204 in) / (8 x 0.375 in)

τ = 12,240 / 3

τ = 4,080 P/in

τ = 4.08 Ksi

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T_2 =T_1 + \dfrac{T_{2s} - T_1}{\eta _c}

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\dfrac{T_{2s}}{T_1} = \left( \dfrac{P_{2}}{P_1} \right)^{\dfrac{k-1}{k} }

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T_{2s} = 579.21 K

T₂ = 300+ (579.21 - 300)/0.8 = 649.01 K

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Given that the pressure ratios across each turbine stage are equal, we have;

\dfrac{T_{5s}}{T_4} = \left( \dfrac{P_{5}}{P_4} \right)^{\dfrac{k-1}{k} }

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\dfrac{T_{7s}}{T_6} = \left( \dfrac{P_{7}}{P_6} \right)^{\dfrac{k-1}{k} }

T_{7s} = 1400×\left( 1/\sqrt{10}  \right)^{\dfrac{0.4}{1.4} }   = 1007.6 K

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Heat supplied is given by the relation

cp(T₄ - T₃) + cp(T₆ - T₅) = 1.005*((1400 - 857.402) + (1400 - 909.5)) = 1038.26349 kJ/kg

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Thermal efficiency of the cycle = (492.9525 )/(1038.26349 ) =0.4748 = 47.48%

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