Design a pipe system to supply water at 20° C from the elevated tank to the demand point at the discharge rate of 2.5 m3/s (see figure below). Take these steps: 1. Identify your system elements. You have 400 m long pipe system that has one 90° bends. 2. Account for minor losses caused by the bend (use K = 0.18), by the valve (use K = 0.2), entrance loss from elevated tank to pipe (use K = 1) and exit loss from pipe to demand point (use K = 0.5) 3. Set the Energy equation to find the total head loss magnitude (hL). 4. Break down the total loss into friction (hf) and minor losses (hM). Use D-W and minor loss equations to find a relationship between Diameter (D) and Friction Factor (f) (both are unknown). In the equation, replace velocity with Q/A to have only D and f as unknowns. 5. Your other equation to find the 2 unknowns is the Moody diagram. Because both equations are non-linear, numerical iteration is needed. After contacting a nearby vendor, you realize that a convenient pipe material is a type of steel with ks = 0.046 mm. 6. Start with assuming f = 0.02. Then, find D using the equation in the previous step (by a numerical solver). Next, find Re and ks/D to follow the Moody diagram for verifying the f value. Iterate until the difference in readings for f is ≤ 0.001. 7. Report D in centimeter after completing the iteration. This is the major outcome of this design problem. Round the D up to the closest commercial size.
Design a pipe system to supply water at 20° C from the elevated tank to the demand point at
the discharge rate of 2.5 m3/s (see figure below). Take these steps:
1. Identify your system elements. You have 400 m long pipe system that has one 90°
bends.
2. Account for minor losses caused by the bend (use K = 0.18), by the valve (use K =
0.2), entrance loss from elevated tank to pipe (use K = 1) and exit loss from pipe to
demand point (use K = 0.5)
3. Set the Energy equation to find the total head loss magnitude (hL).
4. Break down the total loss into friction (hf) and minor losses (hM). Use D-W and minor
loss equations to find a relationship between Diameter (D) and Friction Factor (f)
(both are unknown). In the equation, replace velocity with Q/A to have only D and f
as unknowns.
5. Your other equation to find the 2 unknowns is the Moody diagram. Because both
equations are non-linear, numerical iteration is needed. After contacting a nearby
vendor, you realize that a convenient pipe material is a type of steel with ks = 0.046
mm.
6. Start with assuming f = 0.02. Then, find D using the equation in the previous step (by
a numerical solver). Next, find Re and ks/D to follow the Moody diagram for verifying
the f value. Iterate until the difference in readings for f is ≤ 0.001.
7. Report D in centimeter after completing the iteration. This is the major outcome of
this design problem. Round the D up to the closest commercial size.
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