Respuesta :
Answer with Explanation:
We are given that
Diameter of pipe,[tex]d_1=0.573 m[/tex]
[tex]v_1=13.5 m/s[/tex]
[tex]v_2=5.83 m/s[/tex]
Volume flow rate of the petroleum along the pipe=[tex]Q_{refinery}=A_1v_1=v_(\frac{\pi d^2_1}{4})[/tex]
[tex]Q_{refinery}=13.5\times (\pi\times \frac{0.573)^2}{4})=3.48 m^3/s[/tex]
By equation of continuity
[tex]A_1v_1=A_2v_2[/tex]
[tex]\frac{\pi d^2_1}{4}v_1=\frac{\pi d^2_2}{4}v_2[/tex]
[tex]d^2_2=\frac{v_1}{v_2}d^2_1[/tex]
[tex]d_2=\sqrt{\frac{v_1}{v_2}}d_1[/tex]
[tex]d_2=0.573\sqrt{\frac{13.5}{5.83}}[/tex]
[tex]d_2=0.87 m[/tex]
[tex]d_2=0.87\time 100=87 cm[/tex]
1 m=100 cm
The continuity equation allows to find the results the questions about the pipes and the flow are:
- The flow is: Q = 3.48 m³ / s
- The diameter of the pipe in the refinery is: d₂ = 0.872 m
Given parameters
- Pipe diameter d = 57.3 cm = 0.573 m
- The velocity of the oil is v₁ = 13.5 m / s
- The speed at the refinery v₂ = 5.83 m / s
To find
- The flow.
- The diameter of the refinery pipe.
Fluid mechanics studies the movement of fluids, liquids and gases in different systems, the continuity equation is the conservation of mass for fluids.
[tex]v_1A_1 = v_2A_2[/tex]
Where the subscripts 1 and 2 represent two points of interest, v is the velocity and A is the area.
Let's use the subscript 1 for the pipeline and the subscript 2 for the refinery, let's find the areas.
A₁ = π r₁² = [tex]\pi \frac{d_1^2}{4}[/tex]
A₂ = [tex]\pi \frac{d_2^2}{4}[/tex]π
Let's substitute
[tex]v_1 \pi \frac{d_1^2}{4} = v_2 \pi \frac{d_2^2}{4} \\d_2 = \sqrt{\frac{v_1}{v_2} } \ d_1[/tex]
Let's calculate
d₂ = [tex]\sqrt{\frac{13.5}{5.83} } \ 0.573[/tex]
d₂ = 0.872 m
Flow is constant throughout the pipeline
Q = v₁ A₁
Q = [tex]v_1 \pi \frac{d_1^2}{4}[/tex]
Let's calculate
Q = [tex]13.5 \ \pi \ \frac{0.573^2}{4}[/tex]
Q = 3.48 m³ / s
In conclusion using the continuity equation we can find the results the questions about the pipes and the flow are:
- The flow is: Q = 3.48 m³ / s
- The diameter of the pipe in the refinery is: d₂ = 0.872 m
Learn more here: brainly.com/question/14747327
