Case 21: Water - Three Reservoir Problem 2
Reference: 2500 Solved Problems in Fluid Mechanics and Hydraulics, 1989, McGraw-Hill, Jack B. Evett, Ph. D., Cheng Liu, M.S., Page 309, Example problem 12.11
Pipe Flow Expert File: Case_21_Water_Three_Reservoir_Problem_2.pfe
Problem Description:
Three reservoirs with fluid surface elevations of 15 m, 25 m and 28 m are connected by 3 pipes
Pipe 1 connected to the lowest reservoir is 300 mm diameter x 600 m long.
The internal pipe roughness is 3.0 mm.
Pipe 2 connected to the middle reservoir is 200 mm diameter x 300 m long.
The internal pipe roughness is 1.0 mm.
Pipe 3 connected to the highest reservoir is 200 mm diameter x 1000 m long.
The internal pipe roughness is 1.0 mm.
Calculate the flow rate in each individual pipe.
Calculate the HGL at the pipe junction.
Fluid Data: Water at 10° C (assumed).
Result Comparison:
|
Data Item |
Published data |
Pipe Flow Expert |
|
Pipe 1 Flow rate (l/s) |
-77.8 |
-78.671 |
|
Pipe 2 Flow rate (l/s) |
+46.2 |
+46.662 |
|
Pipe 3 Flow rate (l/s) |
+31.7 |
+32.009 |
|
HGL at Junction (m hd) |
19.7 |
19.811 |
Commentary:
The published data and the calculated results compare well.
Flow to the junction has been indicated by a positive flow rate value.
Flow away from the junction has been indicated by a negative flow rate value.
The method of solution proposed in the text is to assume an elevation for the pipe junction, then calculate the three flow rates.
If the flow rates are not balanced the elevation of the pipe junction is adjusted and the calculation is repeated.
Only three iterations of the node elevation are used in the text 19.0 m, 20.0 m and 19.7 m, the calculation is halted at this point.
Note: The flow balance to and away from the junction is maintained.