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aksik [14]
4 years ago
9

The tank of the air compressor is subjected to an internal pressure of 90 psi. If the inner diameter of the tank is 22 in., and

the wall thickness is 0.25 in., determine the stress components acting at point A. Draw a volume element of the material at this point, and show the results on the element (outer wall).
What would be the maximum shear that this material would experience?

Engineering
1 answer:
Shkiper50 [21]4 years ago
8 0

Answer:

б₁ = 1.98 ksi

б₂ = 1.98 ksi

Explanation:

Calculating the component of stress acting at point A using circumferential stress equation, we have;

б₁ = p*r/t

   = 90*11/0.25

   = 3960 psi = 3.96 ksi

Calculating the component of stress acting at point A using longitudinal stress equation, we have;

б₂ = p*r/2*t

    = 90*11 /2*0.25

    = 1.98 ksi

Find attached of the volume element at point A.

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Water flows in a pipeline. At a point in the line where the diameter is 7 in., the velocity is 12 fps and the pressure is 50 psi
PolarNik [594]

Answer:

a)   P₂ = 3219.11 lbf / ft² , b)    P₂ = 721.91 lbf / ft² , c)  P₂ = 5707.31 lbf / ft²

Explanation:

For this exercise we can use the fluid mechanics equations, let's start with the continuity equation, index 1 is for the starting point and index 2 for the end point of the reduction

     A₁ v₁ = A₂ v₂

     v₂ = v₁ A₁ / A₂

The area of ​​a circle is

    A = π r² = π/4  d²

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    v₂ = 12 (7/3)²

    v₂ = 65 feet / s

Now let's use Bernoulli's equation

     P₁ + ½ ρ v₁² + ρ g y₁ = P₂ + ½ ρ v₂² + ρ g y₂

     P₁ - P₂ = ρ g (y₂ –y₁) + ½ ρ (v₂² - v₁²)

Case 1. The pipe is horizontal, so

      y₁ = y₂

      P₁ - P₂ = ½ ρ  (v₂² –v₁²)

      P₂ = P₁ - ½ ρ (v₂² –v₁²)

     ρ = 62.43 lbf / ft³

     P₁ = 50 psi (144 lbf/ ft² / psi) = 7200 lbf / ft²

    P₂ = 7200 - ½ 62.43 / 32 (65² -12²)

    P₂ = 7200 - 3980.89

    P₂ = 3219.11 lbf / ft²

Case 2 vertical pipe with water flow up

        y₂ –y₁ = 40 ft

        P₁ - P₂ = ρ g (y₂ –y₁) + ½ rho (v₂² - v₁²)

        7200 - P₂ = 62.43 (40) + ½ 62.43 / 32 (65 2 - 12 2) =

        P₂ = 7200 - 2497.2 - 3980.89

         P₂ = 721.91 lbf / ft²

Case 3. Vertical water pipe flows down

         y₂ –y₁ = -40

         P₂ = 7200 + 2497.2 - 3980.89

         P₂ = 5707.31 lbf / ft²

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