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
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.