Question

A round pipe of varying diameter carries petroleum from a wellhead to a refinery. At the wellhead, the pipe's diameter is 56.3 cm ( 0.563 m) and the flow speed of the petroleum is 12.3 m/s. At the refinery, the petroleum flows at 5.03 m/s. What is the volume flow rate of the petroleum along the pipe and what is the pipe's diameter at the refinery?

volume flow rate: m3/s

diameter: cm

Answer 1

Volume flow rate is given by:

Q1 = Volume flow rate = V1*A1

V1 = flow speed at well head = 12.3 m/sec

A1 = pipe's area at wellhead = pi*d^2/4

d1 = diameter = 0.563 m

So,

Q1 = (12.3 m/sec)*pi*0.563^2/4

Q1 = 3.06 m^3/sec = flow rate of petroleum along the pipe

Part B.

Using Continuity equation

Q1 = Q2

flow rate at wellhead = flow rate at refinery

A1*V1 = A2*V2

pi*d1^2*V1/4 = pi*d2^2*V2/4

d2 = d1*sqrt (V1/V2)

Given that

V2 = flow speed at refinery = 5.03 m/sec

So,

d2 = 0.563*sqrt (12.3/5.03)

d2 = diameter at refinery = 0.880 = 88.0 cm

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