1 answer

A round pipe of varying diameter carries petroleum from a wellhead to a refinery. At the...

Question:

A round pipe of varying diameter carries petroleum from a wellhead to a refinery. At the wellhead the pipe\'s diameter is 52.9 cm and the flow speed of the petroleum is 13.7 m/s. At the refinery the petroleum flows at 5.75 m/s. What is the volume flow rate of the petroleum along the pipe and what is the pipe\'s diameter at the refinery?


Answers

(a) At the wellhead, diameter of the pipe, d1 = 52.9 cm = 0.529 m

at this location, flow speed, v1 = 13.7 m/s

Now, expression for the volume flow rate at a point is given by -

V_dot = v*A [A = cross-sectional area of the pipe]

Now,

A = pi*d^2/4

A1 = pi*(0.529 m)^2 / 4 = 0.22 m^2

So,

V_dot = 13.7 m/s * 0.22 m^2 = 3.01 m^3/s

Since, volume flow rate is the same throughout the pipe, hence volume flow rate at refinery = 3.01 m^3/s (Answer)

(b) Now, as we have discussed above, volume flow rate is the same throughout,

So,

V_dot1 = V_dot2

=> v1*A1 = v2*A2

=> v1*pi*d1^2/4 = v2*pi*d2^2/4

=> v1*d1^2 = v2*d2^2

=> d2 = d1*sqrt(v1/v2)

= 52.9 cm * sqrt(13.7 m/s / 5.75 m/s) = 81.7 cm

Therefore, pipe's diameter at the refinery = d2 = 81.7 cm (Answer)

.

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