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Please show ALL work, I want to see all the steps. Please contact me for extra d

ID: 2995518 • Letter: P

Question

Please show ALL work, I want to see all the steps. Please contact me for extra details if needed on here.

Five oil fields, each producing an output of Q barrels per day, are connected to a 28-in. diameter "main line" (A-B-C) by 15-in. diameter "lateral pipes" as shown. The friction factor is the same for each of the pipes and elevation effects are negligible. For section A-B determine the ratio of the pressure drop per mile in the main line to that in the lateral pipes. Repeat the calculations for section B-C.

Explanation / Answer

Pressure drop = fL/D *(1/2)*rho*V^2

V = Q/A = Q / (pi/4 *D^2) = 4Q / (pi*D^2)

Thus pr drop = fL/D *(1/2)*rho* [4Q / (pi*D^2)]^2

Pr drop = fL/D *(1/2)*rho*16*Q^2 / (pi^2 *D^4)

Pr drop = 8*rho*Q^2 *f*L / (pi^2 *D^5)

So pressure drop is proportional to Q^2 / D^5.

a)

In section AB, flow rate = 3Q.

Pr drop in main line / Pr drop in lateral line = [(3Q)^2 / 28^5] / [Q^2 / 15^5]

= 0.3971

b)

In section BC, flow rate = 5Q.

Pr drop in main line / Pr drop in lateral line = [(5Q)^2 / 28^5] / [Q^2 / 15^5]

= 1.103

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