Question

An engineer needs to determine the size of a pipe required to carry sewerage away from a street in a new development. There are 40 single family residences planned for the street and the average family size is 4 ½ persons. The average daily water usage is estimated at 70 gallons per person. Assume that all water used is discharged to the sewer. The amount of water, Q, in ft3/sec, that a pipe flowing full can accommodate is given byQ = 0.432CD2.63S0.54whereC is a coefficient that depends on the roughness of the inside of the pipe, S depends on the slope of the pipe and D is the inside diameter of the pipe, measured in feet.. For this project concrete-lined pipe is to be used so that C = 120, and for the street S = 0.15ft/ft. 1)Write Q as a function of D.2)If the pipe is only available in size of 2” to 24” in inside diameter in increments of 2”, plot Q as a function of D for the range of available pipe sizes.Use the vertical line test to determine if the curveis the graph of a function. Select the correct pipe size that should be used for the sewer line (1) based on the average discharge flow rate (2) based on a Super bowlhalftime discharge flow which is twelve times the average discharge rate.

Answer 1

1)Q= 18.61D^2.63

where D is in feet and Q is in ft³/sec

2)use 2" size pipe based on the average discharge flow rate

use pipe size between 2" to 4" based on the super bowlhalftime discharge flow

in the question, it is given that estion, it is given that there are 40 single family residences and average family size is 4112 i population - 40x4's - 180 ye dally water usage = fo gallons per person given in the queshon) average water usage - 180x80 = 12600 gallon per day = 12600 X 0.00 3785411484 I gallon = 24X60X60 0.003785911784 m = 5:52x104 m3/sec. Assuming that all water used is discharge to on used is dischavao to I I im=3.28ft] Sewer I given in the question) average sewage flow = avevage water usage - 5.59x104 m3/sec 5.528104 x 3.28 = 0.01948 ft3/ec. super bowl half time discharge = lax average flow (given in the = 12x and the xo.01948 queswon = 0.23376 ft3 - Sec The discharge that the pipe flowing full can accomadate is given by a = 0.432 x C x D x 5 34 (given in the question) lao C - Roughness coeficient s- Slope factor -0.15 O Diameter of pipe in feet :4 2.63 2.63 where D is in G-0432 x 120 x 0.15 D = 18.61 Ď feet Q is in ft/sec 2.63 0.54

- 2 pipe is available in standard sizes of a to 24" (2 inches to I 24 inches) I inch = 0.0833 feet for D = 2 inch 263 Q = 18 61 x (2x0:0833) - 0.167 ft²/sec Similary for all values of D, we can find a which is shown in the table. I d (inches) I Q (ft3/sec) 0-167 P. 0338 3.0031 6.406 11.soq 18.61 27.91 39.654 54 71.244 arsy 115.06 A graph was plotted between Q and 'd from the graph, We can get the pipe size based on average flow rate and super bowl half time discharge 0 for a = average sewage flow 0.01948 ft3/sec , the pipe size should be less than a inches approximately take a size pipe. ② for a super bowl half time discharge - 0.23376 ft /sec. the pipe size should be between a" to 4"

(ft3/seca Q ô 8 8 e o o 3 4 6 8 a 24 10 1 D "Iniche