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 ofSectional 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 tailing1 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 ofFlow 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.

HMD =A/P

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).

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.