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Andrews [41]
3 years ago
6

A cylindrical tank is required to contain a gage pressure 520 kPa . The tank is to be made of A516 grade 60 steel with a maximum

allowable normal stress of 150 MPa . If the inner diameter of the tank is 2.6 m , what is the minimum thickness, t, of the wall? Express your answer with appropriate units to three significant figures.
Engineering
1 answer:
enot [183]3 years ago
4 0

Answer:

t= 4.5 mm

Explanation:

Given that

P = 520 KPa ( gauge)

Maximum allowable normal stress ,σ= 150

d= 2.6 m

Wall thickness = t

The normal stress for pressure vessel given as

\sigma=\dfrac{Pd}{2t}               ( hoop stress)

We always take maximum stress for safe design.

\sigma=\dfrac{Pd}{2t}

Now by putting the values

150\times 1000=\dfrac{520\times 2.6}{2t}

t= 4.5 mm

So the minimum thickness, t, of the wall is 4.5 mm

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Explanation:

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The term sin(30) is because of the slope of the wall

The pressure of water is:

p(y) = SGw * (h - y)

Then:

T1 = \int\limits^h_0 {SGw * (h-y) * sin(30) * L * (h-y)} \, dy

T1 = \int\limits^h_0 {SGw * sin(30) * L * (h-y)^2} \, dy

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T1 = SGw * sin(30) * L * \int\limits^h_0 {(h-y)^2} \, dy

T1 = SGw * sin(30) * L * \int\limits^h_0 {h^2 - 2*h*y + y^2} \, dy

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T1 = SGw * sin(30) * L * (h^2*h - h*h^2 + 1/3*h^3)

T1 = SGw * sin(30) * L * (h^3 - h^3 + 1/3*h^3)

T1 = 1/3 * SGw * sin(30) * L * h^3

To remain stable the equilibrant torque (Teq) must be of larger magnitude than the water pressure torque (T1)

1/4 * b^2 * h * L * SG > 1/3 * SGw * sin(30) * L * h^3

In an equilateral triangle h = b * cos(30)

1/4 * b^3 * cos(30) * L * SG  > 1/3 * SGw * sin(30) * L * b^3 * (cos(30))^3

SG > SGw * 4/3* sin(30) * (cos(30))^2

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