Flu. 810  Data for Calculating Flow In Circular Sewers.

Flu. 810 -Data for Calculating Flow In Circular Sewers.

C.C = carrying capacity. H. = height in feet; D. - diameter or width at springing in feet; P.c.c. = proportional earning capacity (the width, D, at springing of the arch = 1 in each case); S.A.P. -sectional area of flow in square feet; w.p.=wetted perimeter in feet; h.m.d. = hydraulic mean depth in feet

The efficiency of 4-inch, 6-inch, and 9-inch pipes at the respective gradients of 1 in 40, 60, and 90, and at various depths of flow, is shown in Table XXVI.

Table XXVI. Hydraulic Mean Depth, Velocity, Discharge, Ad, Of 4, 6, And 9-Inch Circular Drains

Proportion of

Sectional Area occupied by the flow

Depth in Inches.

Sectional Area of flow in square feet

H.M D in feet

v.

In feet per minute.

D.

in cubic feet per minute.

9-inch pipes falling 1 in 90.

Full

9

•442

187

257.0

114

3/4

6 3/4

.355

•225

291.1

1039

2/3

5 2/5

•309

•216

2834

881

1/2

4 1/2

221

•187

257 0

57

1/3

3 3/5

127

138

2100

26 8

1/4

2 1/4

•086

109

179.9

15.6

6 inch pipes tailing

1 in

Full

6

19634

•125

240

471

3/4

4 1/2

•158

•1508

272

424

2/3

3 5/4

139

14f>6

265

354

1

3

•09817

.125

240

235

1/5

•0573

0931

196

11.0

1/4

1 1/2

•0384

•0733

168

64

4 inch pipes tailing 1 in 40.

Full

4

•0873

0835

224

196

3

•0762

1006

254

178

2/3

2 2/5

0618

•0970

247

151

i

2

•0436

•0835

224

9.8

I

1 3/5

0255

•0621

183

4 6

1/4

1

•017

•0489

157

2.7

For other sizes of circular drains, the calculations will be simplified by the use of the following table: -

Table XXVII.1 Data For Calculating Flow In Circular Drains

Depth of

Flow

Area.

Wetted Perimeter

H.M.D.

Full

•7854 d2

3.1416d

.25d

|

•632 d2

2.095 d

.296d

•556 d2

1.911d

•292 d

1/2

•393d2

1.571d

•25 d

1/3

.229 d2

1.231d

•186d

1/4

.154d2

1.047d

.147d

1 This table is taken from The Sewerage Engineer'sNote-Book,by Albert Wollheim, Assoc.M.Inst.C.E.

When it is required to ascertain the discharge of a pipe at any specific depth of flow, the following formula may be used: -

A - Sectional area of flow. P = Wetted perimeter. HMD= Hydraulic mean depth.

r- radius. d - diameter. = ratio between diameter and circumference, or 1:3 1410.

Table XXVII 1 Data For Calculating Flow In Circula 30071

HMD =A/P

Table XXVII 1 Data For Calculating Flow In Circula 30072Fig. 311.   Diagram to ILLUSTRATE Trig, onometrical Calculations of the Dis charge frum a Circular Drain

Fig. 311. - Diagram to ILLUSTRATE Trig, onometrical Calculations of the Dis-charge frum a Circular Drain.

(.Semi-chord c may be found by right-angled trigonometry).

Table XXVII 1 Data For Calculating Flow In Circula 30074

Perimeter of segment = number of degrees x .017453 radius.

Those not accustomed to the use of trigonometry may find the following method of solution of the problems somewhat simpler: -

KT = radius of circle. N O T = chord of whole arc. N Q = chord of half arc. O Q = versed sine (or depth of flow). N TQ = segment.

From NK2 subtract OK2, and the square root of the remainder = ON = 1/2NT.

N Q may he found from the following, - N Q =√ON2+ OQ2. Wetted Perimeter NQ T = (8 NQ-NT)/ 3.

Area of Segment N TQ = 2/3 (N T x O Q) +OQ3/2NT

Fig 312.   Diagram to Illustrate Arith. metical Calculation of the Discharge from a Circular Drain.

Fig 312. - Diagram to Illustrate Arith. metical Calculation of the Discharge from a Circular Drain.