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Terminal VelocityD epending upon the rate of flow from the branch drain

into the stack, the type of stack fitting, the diam eter of the

stack, and the flow dow n the stack from upper levels, the

discharge from the branch m ay or m ay not entirely fill the

cross-section of the stack at the point of entry. As soon as

the w ater enters the stack it is im m ediately accelerated at

the rate of 82.2 feet/second/second by the force of gravity,

and in a very short distance form s a sheet around the innerw all of the pipe. It can be sim ply described as a hollow

cylinder of w ater. This sheet of w ater w ith a core of air in

the center continues to accelerate until the frictional force

exerted by the pipe w all on the falling sheet of w ater

equals the gravitational force. The frictional force varies as

the square of the velocity, and thus resistance to flow is

very rapidly increased. From the point w here frictional

force equals gravitational force, the sheet of w ater w ill con-

tinue to fall at a velocity w hich rem ains practically un-

changed. This ultim ate vertical velocity is called term inal

velocity,and the distance in w hich this m axim um veloci-

ty is achieved is called the term inal length.

F.M . D aw son and A.A. Kalinske in Report on H ydraulics

and Pneum atics of Plum bing D rainage System s(State

U niversity of Iow a, Studies in Engineering B ulletin 10,

1987) and R.S. W yly and H .N . Eaton in Capacities of

Plum bing Stacks in B uildings(N ational Bureau of

Standards Building M aterials and Structures Report BM 132,

1952) have investigated term inal velocity and derived a

w orkable form ula by treating the sheet of w ater as a solid

hollow cylinder sliding dow n the inside w all of the pipe.

The form ulas developed for term inal velocity and term inal

length, w ithout going through the com plicated calculus in-

volved, are

V t= 3.0 (q/d)2/5

Lt = 0.052 V2t

w here: V t = term inal velocity in stack, fps

Lt = term inal length below point of flow entry, ft

q = quantity rate of flow , gpm

d = diam eter of stack, in.

Applying the form ulas for various size stacks, it is found

that term inal velocity is achieved at approxim ately 10 to 15

fps and this velocity is achieved w ithin 10 to 15 feet of fall

from point of entry. The im portance of this research is that

it conclusively destroys the m yth that w ater falling in a stack

from a great height w ill destroy the fitting at the base of the

stack. The velocity at the base of a 100-story stack is only

slightly and insignificantly greater than the velocity at the

base of a three-story stack! There is no scientific reason for

lim iting the height of a soil or w aste stack of any size and

the stacks can be run straight dow n, w ithout offsets, for 1000

feet or m ore w ith the utm ost confidence. So-called velocity

breaksare absolutely unw arranted and, in fact, could cause

excessive pneum atic pressure fluctuations in the stack.

Stack OffsetsM ost engineers are aw are of the problem w hich exists

w henever a stack offsets at an angle greater than 45 de-

grees. At the point of offset, flow enters the horizontal drain

at a relatively high velocity w hen com pared to the velocity

of flow in a horizontal drain under uniform flow conditions

at full or half-full flow . W hen the w ater reaches the bend

at the offset it is turned at right angles to its original flow ,

and for a few pipe diam eters dow nstream it w ill continue

to flow at relatively high velocity along the low er part ofthe horizontal pipe.

Since the slope of the horizontal piping is not adequate

to m aintain the velocity of flow that existed w hen the w a-

ter reached the offset, the velocity of flow in the horizontal

drain slow ly decreases w ith a corresponding increase in the

depth of flow until a critical point is reached w here the

depth of flow suddenly and sharply increases. This increase

in depth is often great enough to com pletely fill the cross

sectional area of the pipe. This sudden rise in depth is

called the hydraulic jum p(Figure 1). The critical distance

at w hich the hydraulic jum p m ay occur varies. It is de-

pendent upon the entrance velocity, depth of w ater w hichm ay already exist in the horizontal drain w hen the new

flow is introduced, roughness of the pipe, diam eter of the

pipe and the slope. The distance varies from im m ediately

at the stack fitting up to ten tim es the diam eter of stack

dow nstream : Less jum p occurs if the horizontal drain is

larger in size than the stack. Increasing the slope of the hor-

izontal drain w ill also m inim ize the jum p. After the hy-

draulic jum p occurs and fills the drain, the pipe tends to

High-Rise DWV and Storm SystemsAlfred Steele, PE CIPE

O ne of the oldest and m ost persistent m yths in the plum bing profession is the belief that extrem ely high velocities de-

velop in the stacks of high-rise buildings. The plum bing engineer is invariably asked how he is going to provide for these

velocities at the base of the stack. H ow is he going to prevent the base fitting from being blow n out or broken? N o spe-

cial provisions are required for trem endous velocities, and no special precautions are required to protect the base fitting.

Excessive velocities just do not occur!

54 Plumbing Systems & Design Sept/O ct 2003

C o n t i n u i n g E d u c a t i o n

Repri n ted fr om Al fr ed Steele (1984), Advanced Plum bing Technology, Elmhu rst, IL: Constru ction In du stry Press.


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Sept/O ct 2003 Plumbing Systems & Design 55

flow full, w ith large bubbles of air m oving along the top of

the pipe w ith the w ater. Surging flow conditions w ill exist

until the frictional resistance of the pipe retards the veloci-

ty to that of uniform flow conditions. Any offset of the

stack, at any floor of the building, greater than 45 degreescan cause hydraulic jum p.

W hen the hydraulic jum p occurs, and proper venting has

not been provided, trem endous pneum atic pressures are

built up in the area behind the jum p. There have been cas-

es w here this excess pressure (greater than a one-inch col-

um n of w ater) has extended 40 feet up the stack. It m ust

be stressed that this excess pressure occurs only w hen ad-

equate venting has not been provided. U nder no circum -

stances should the fixtures on the floor directly above an

offset connect to the stack before the offset. These fixtures

should be piped and connected to the horizontal offset

m ore than ten stack diam eters dow nstream or preferablyconnected to the vertical at least tw o feet below the hori-

zontal offset (Figure 2).

Sizing Offset StacksM any high rise buildings decrease the floor areas at cer-

tain specified heights. To accom m odate the decreased ar-

eas, fixture layouts are changed and stacks m ust be offset

to new locations. There is an acceptable m ethod of sizing

offset stacks w hich can result in substantial econom ies.

Figure 3illustrates a typical offset stack. The procedure for

sizing is as follow s:

1. Size the portion above the offset as for a regular stack

based upon the total num ber of fixture units abovethe offset.

2. Size the horizontal offset as for a building drain.

3.The portion of the stack below the offset shall be at

least the size of the offset or based upon the total

num ber of fixture units on the entire stack (both

above and below the offset), w hichever is the larger.

Expansion and ContractionExpansion and contraction of stacks is another question

alw ays brought up for consideration. There has not been

an actual docum ented instance of stack failure due to ex-

pansion or contraction of a stack caused by a variation in

tem perature. The flow of w ater is not constant enough tokeep it in contact w ith the pipe long enough for the trans-

fer of necessary heat to affect the pipe. O f far greater im -

portance and danger in a high-rise building, and it is a

problem w hich is often overlooked, is the shrinkage in

height of the low er stories of the building. As the gross

w eight of the upper structure is added, foreshortening at

the low er floors has been noted to be as m uch as tw o inch-

es in a sixty story building. Soluble gaskets installed in the

caulked joints have obviated this problem . The structural

engineer should alw ays be consulted to determ ine the ex-

tent of foreshortening to be expected.

Suds PressureThe prevalent use of high-sudsing detergents in w ashing

m achines, dishw ashers, laundry trays and kitchen sinks has

created serious problem s in all residential buildings and es-

pecially in high-rise buildings. U ntil m anufacturers are

forced to m arket only detergents w ithout sudsing charac-

teristics the plum bing engineer m ust understand and cope

w ith the dangers created in the sanitary system by the pres-

ence of suds. (An interesting sidelight: suds, in and of

them selves, do not enhance the cleaning ability of soaps or

detergents in any w ay).

Figure 1. Hydraulic Jump at Offset Figure 2. Piping for Fixtures Directly Above Offset


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C o n t in u in g E d u c a t io n : H ig h - Rise D W V a n d S t o r m S y st e m s

56 Plumbing Systems & Design Sept/O ct 2003

W hen the flow of w astes from upper floors contains deter-

gents, the suds-producing ingredients are vigorously m ixed

w ith the w ater and air in the stack as the w aste flow s dow n

the stack and further m ixing action occurs as other branch

w aste discharges m eet this flow . These suds flow dow n the

stack and settle in the low er sections of the drainage system

and at any offsets greater than 45 degrees in the stack.

Investigation has show n that w here sudsing w astes are pres-

ent the sanitary and vent stacks are laden w ith suds, and this

condition w as found to exist for extended periods of tim e.

Liquid w astes are heavier than suds and easily flow

through the suds-loaded drainage piping w ithout carrying

the suds along w ith the flow . Everyone is aw are of the dif-

ficulty of flushing the suds out of a sink. The w ater sim ply

flow s through the suds and out the drain, leaving the m a-

jor portion of the suds behind. The sam e action occurs in

the low er sections of the drainage system except for one

im portant difference: air, as w ell as w ater, is now flow ing

in the piping. This air, w hich is carried dow n w ith the

w aste discharge, com presses the suds and forces them to

m ove through any available path of relief. The relief path

m ay be the building drain, any branches connected to the

building drain, the vent stack, branch vents, individual

vents or com binations of any of the foregoing. A path of re-

lief m ay not alw ays be available, or could be cut off or re-

stricted by the hydraulic jum p, or a path m ay just be inad-

equate due to location or size. If one or m ore of these con-

ditions exist, excessively high suds pressure can develop

and blow the seals of traps w ith the accom panying ap-

pearance of suds in fixtures.

H igh suds pressure zones occur at every change in di-

rection, vertically or horizontally, w hich is greater than 45

degrees. W here vent stack base connections, relief vents,

branch vents or individual vents serve as the relief path for

the high suds pressure, they are usually found to be inad-

equate in size w ith resultant suds conditions appearing at

the fixtures. The vent pipe sizing tables in practically every

code are calculated on the basis of air flow capacity and do

not in any w ay provide for the m ore dem anding flow of

suds. Sizes w hich are based on these code tables are inad-

equate to accom m odate suds flow and thus are incapable

of providing adequate suds pressure relief.

Suds are m uch heavier than air and consequently do notflow w ith the sam e ease. They produce a m uch greater fric-

tion head loss for the sam e rate of flow . The density of old

or regenerated suds varies from 2 pounds per cubic foot to

a high of 19 pounds per cubic foot, dependent upon the

detergent used. For equal rates of flow and pressure loss,

the vent pipe diam eter for suds relief flow m ust be from 20

to 80 per cent greater than for air flow .

W henever a soil or w aste stack receives w astes from

w ashing m achines, dishw ashers, laundry trays, kitchen

Figure 3. Sizing of Stack with an Offset Figure 4. Suds Pressure Zones


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sinks or other fixtures w here sudsing detergents are used,

the drainage and vent piping for the low er floor fixtures or

for the fixtures above offsets m ust be arranged to avoid

connection to any zone w here suds pressure exists.

Suds pressure zones exist in the follow ing areas:

1. At a soil or w aste stack offset greater than 45 degrees:

40 stack diam eters upw ard and 10 stack diam eters hori-

zontally from the base fitting for the upper stack sec-

tion. A pressure zone also exists 40 stack diam eters. up-

stream from the top fitting of the low er stack section.

2.At the base of a soil or w aste stack: The suds pres-

sure zone extends 40 stack diam eters upw ard from

the base fitting.

3.In the horizontal drain from the base of a stack: The

suds pressure zone extends 10 stack diam eters from

the base fitting, and w here an offset greater than

45 degrees in the horizontal occurs, the

pressure zones extend 40 stack diam e-

ters upstream and 10 diam eters dow n-

stream from the offset fitting.

4. In a vent stack connected to a suds

pressure zone: The suds pressure zone

exists from the vent stack base connec-

tion upw ard to the level of the suds

pressure zone in the soil or w aste stack.

Figure 4 illustrates all the above zones.

Vent SystemThe design of vent stacks for high-rise

buildings conform s to the design criteria

established for any building w ith slight ad-

ditional precautions. It is im portant to un-

derstand that the sole purpose of a vent

stack is to relieve excessive pressure fluc-

tuations in the soil or w aste stack it serves.

Just as the flow of w ater obeys all the law s

of hydraulics so does the flow of air obeyall the gas law s. The length of run and size

of pipe should be designed to m aintain

pressure fluctuations in the sanitary system

w ithin lim its to m aintain a m axim um pres-

sure variation of plus or m inus one-inch

colum n of w ater at fixture traps.

W hen w ater is flow ing in the sanitary

system , pressures in the drainage and vent

stacks of a m ulti-story building are con-

stantly fluctuating. The vent stack connec-

tion at the base of the drainage stack and

the branch vent connections to the branchdrains cannot alw ays elim inate these fluc-

tuations. For reasons w hich have not as yet

been determ ined, excessive pressure fluc-

tuations occur in stacks w hich have m ore

than ten branch intervals. It then becom es

extrem ely im portant to balance pressures

throughout the drainage stack by m eans of relief vents lo-

cated at various intervals. D rainage stacks in buildings hav-

ing m ore than ten branch intervals should be provided w ith

a relief vent at each tenth interval, counting from the top-

m ost branch dow nw ard. The low er end of the relief vent

should connect to the soil or w aste stack below the

drainage branch connection and the upper end should

connect to the vent stack at least three feet above floor lev-

el.Figure 5 illustrates m ethods of providing relief vents at

stack offsets and Figure 6 illustrates relief vents for stacks

having m ore than 10 branch intervals.

The vent-sizing tables in m any existing codes do not list

the size of pipe required for the exceptionally long lengths

of run encountered in high-rise construction. U tilization of

the follow ing form ula w ill result in the m axim um perm issi-

ble length.

Figure 5. Venting at Stack Offsets


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An expansion joint or offset should alw ays be provided

at the connection to roof drains. This is required to prevent

pipe expansion from raising the roof drain and destroying

the integrity of the w aterproofing of the roof. Storm w ater

piping is probably subjected to the m ost frequent m ove-m ent of any plum bing system , but not necessarily the m ax-

im um expansion. The m ovem ent is due to the frequently

changing difference in the outside tem perature relative to

the inside tem perature. In w inter, m elting snow and ice at

low tem peratures flow into the drain

w here the piping is surrounded by an

am bient tem perature of 70 degrees or

higher.

Low tem perature liquid flow in the

storm w ater piping w ill cause condensa-

tion to form on the outside of the piping

in the building. It is therefore advisableto insulate all storm w ater offsets to pre-

vent condensation from staining ceilings.

The storm w ater system for high-rise

construction is usually adequately cov-

ered by code, but there are m any

codes w hich do not cover, and there-

by by om ission do not perm it the in-

stallation of controlled-flow roof

drainage. It is w ell w orthw hile dis-

cussing the use of controlled-flow roof

drainage w ith the authorities if it is not

covered by their code. Controlled-flow

roof drainage has advantages to rec-

om m end it, in lieu of conventional

roof drainage, in m ost applications. It

is especially advantageous for high-

rise construction. The higher the build-

ing, the m ore econom ical its use be-

com es. Econom y is of prim e im por-

tance to the builder, but of even far

m ore im portance than the econom ies

realized, controlled-flow roof drainage

is one of the best w ays to com bat w a-

ter pollution and flooding during

heavy rainfalls. It is the authors con-sidered opinion that every m unicipali-

ty should m ake it m andatory to use

controlled-flow roof drainage w here

com bined public sew ers are utilized.

H ere is an ideal and practical m ethod

of fighting pollution w hich does not

cost the com m unity one red cent!

D uring heavy storm s, sew age treat-

m ent plants cannot handle the increased flow s and conse-

quently trem endous quantities of untreated raw sew age are

dum ped into the nations stream s, lakes or oceans. W here

separate public storm and sanitary sew ers are available, itis still desirable to use controlled-flow as a m eans of alle-

viating flooding. By lim iting the quantity of flow into the

storm sew ers during heavy storm s, the sew ers are better

able to handle the runoff from other areas.

Figure 7 . Typical Wet Stack

Table 1. Fixture Units for Wet Stacks

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