Page 845 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

800 Appendix D: Fluid Mechanics—Reviews of Selected Topics

TABLE CDD.2(a)
Spreadsheet Calculating Pressure Surface for Under-Drain System (Excerpt)
Formulae
Q(orifice)j j 1 ¼ A(orif) C (2g)0.5 (DHi, j)0.5
*
*
Q(loss)j j 1 ¼ A(orif) C (2g)0.5 (DHi, j)0.5 n(orifices)=L DL
Q(lat)j j 1 ¼ Q(lat)j 1 Q(loss)j j 1
v(lat)j j 1 ¼ Q(lat)j j 1=A(lat)
2
*
DhLj j 1 ¼ f(yj j 1=d(lat) (v j =2g)
Scenario
(1) Data entries are to develop model (they are not realistic)
(2) Under-drain system is generic with plastic pipe assumed for header and laterals
(3) Lateral missing for x ¼ 0 m; also add laterals such that x y

Data Inputs
Data-Header Data—Laterals Data—Orifices
f ¼ 0.012 f ¼ 0.012 C ¼ 0.620
3
3
Q(header) ¼ 1.00 m =s Q(lateral) ¼ 0.20 m =s d(orifice) ¼ 0.005 m
L(header) ¼ 10 m L(lateral) ¼ 15 m n(orifices)=L ¼ 55 orifices=m
d(header) ¼ 0.50 m d(lateral) ¼ 0.25 m n(orifices) ¼ 825 orifices
g ¼ 9.808 m=s 2 n(laterals) ¼ 5 Q(orifice) ¼ A(orif) C (2g) 0.5 (DHi, j) 0.5
H ¼ 20.000 m

Preliminary Calculations

Lateral # A 1 2 3 4 5
x(header) m 0.00 2.00 4.00 6.00 8.00 10.00
3
Q(header) m =s 1.00 0.8 0.6 0.4 0.2 0
v(header) m=s 5.093 4.074 3.056 2.037 1.019 0.000
Dh L (header) m 0.063 0.041 0.023 0.010 0.003 0.000
H m 20.000 19.937 19.896 19.873 19.863 19.860

TABLE CDD.2(b)
Abstract of Head Levels and Flows in Header Pipes and Laterals for a Filter Bed a

1.0 2.0 5.0
x (m) Q(lat) j j 1 H(i, j) p(i, j) Q(lat) j j 1 H(i, j) p(i, j) p(i, j)
3
3
Y (m) (m =s) (m) (m) (m =s) (m) (m) (m)
0.0 0.200 19.937 13.090 0.200 19.896 13.050 Columns 3.0 m 13.014
1.0 0.187 19.899 13.161 0.187 19.858 13.120 and 4.0 m 13.084
2.0 0.174 19.866 13.229 0.174 19.825 13.188 omitted 13.152
3.0 0.160 19.838 13.294 0.160 19.797 13.253 13.217
Rows 4.0 m to 12.0 m not shown

13.0 0.028 19.734 13.717 0.029 19.693 13.676 13.640
14.0 0.015 19.734 13.729 0.016 19.693 13.688 13.652
15.0 0.002 19.734 13.733 0.002 19.693 13.693 13.657

a
Coarse grid—abstracted from Table CDD-2(a).