A round pipe of varying diameter carries petroleum from a wellhead to a refinery. At the wellhead, the pipe's diameter is 57.3 cm ( 0.573 m) and the flow speed of the petroleum is 13.5 m/s. At the refinery, the petroleum flows at 5.83 m/s. What is the volume flow rate of the petroleum along the pipe and what is the pipe's diameter at the refinery?

The continuity equation allows to find the results the questions about the pipes and the flow are:

Given parameters

To find

Fluid mechanics studies the movement of fluids, liquids and gases in different systems, the continuity equation is the conservation of mass for fluids.

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 =  

         A₂ = π  

Let's substitute

Let's calculate

       d₂ =  

       d₂ = 0.872 m

Flow is constant throughout the pipeline

       Q = v₁ A₁

       Q =

Let's calculate

        Q =  

         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:

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Answer with Explanation:

We are given that

Diameter of pipe,

Volume flow rate of the petroleum along the pipe=

By equation of continuity

1 m=100 cm

the maxium height is 34m/s