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lys-0071 [83]
3 years ago
10

A round pipe of varying diameter carries petroleum from a wellhead to a refinery. At the wellhead, the pipe's diameter is 50.9 c

m ( 0.509 m) and the flow speed of the petroleum is 11.5 m/s. At the refinery, the petroleum flows at 5.25 m/s. What is the volume flow rate of the petroleum along the pipe and what is the pipe's diameter at the refinery
Physics
1 answer:
seraphim [82]3 years ago
6 0

Answer:

Flow rate 2.34 m3/s

Diameter 0.754 m

Explanation:

Assuming steady flow, the volume flow rate along the pipe will always be constant, and equals to the product of flow speed and cross-section area.

The area at the well head is

A = \pi r_w^2 = \pi (0.509/2)^2 = 0.203 m^2

So the volume flow rate along the pipe is

\dot{V} = Av = 0.203 * 11.5 = 2.34 m^3/s

We can use the similar logic to find the cross-section area at the refinery

A_r = \dot{V}/v_r = 2.34 / 5.25 = 0.446 m^2

The radius of the pipe at the refinery is:

A_r = \pi r^2

r^2 =A_r/\pi = 0.446/\pi = 0.141

r = \sqrt{0.141} = 0.377m

So the diameter is twice the radius = 0.38*2 = 0.754m

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Answer:

v  = 2.8898 \frac{m}{s}

Explanation:

This is a problem easily solve using energy conservation. As there are no non-conservative forces, we know that the energy is conserved.

When the spring is compressed downward, the spring has elastic potential energy. When the spring is relaxed, there is no elastic potential energy, but the pellet will have gained gravitational potential energy and kinetic energy. Lets see what are the terms for each of this.

<h3>Elastic potential energy</h3>

We know that a spring following Hooke's Law has a elastic potential energy:

E_{ep} = \frac{1}{2} k (\Delta x)^2

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To obtain the spring's constant, we know that Hooke's law states that the force made by the spring is :

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as we need 9.12 N to compress 4.60 cm, this means:

k = \frac{9.12 \ N}{4.6 \ 10^{-2} \ m}

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So, the elastic energy of the compressed spring is:

E_{ep} = \frac{1}{2} 198.26 \ \frac{ N}{m} (4.6 \ 10^{-2} \ m)^2

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<h3>Gravitational potential energy</h3>

To see how much gravitational potential energy will the pellet win, we can use

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Taking all this together, the gravitational potential energy when the spring is relaxed will be:

\Delta E_{gp} = 4.97 \ 10^{-3} kg \ 9.8 \frac{m}{s^2} 4.6 \ 10^{-2} m

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We know that the kinetic energy for a mass m moving at speed v is:

E_k = \frac{1}{2} m v^2

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E_k = \frac{1}{2} \ 4.97 \ 10^{-3} kg \ v^2

<h3>All together</h3>

By conservation of energy, we know:

E_{ep} = \Delta E_{gp} + E_k

0.209759 \ Joules = 0.00224 \ Joules + \frac{1}{2} \ 4.97 \ 10^{-3} kg \ v^2

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