# Energy losses and pressure head changes at storm drain junctions

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An investigation has been made of the magnitude of
hydraulic losses produced by storm drain junction
structures which connect pipes operating under f1owfull
conditions.
The study comprised three parts:
(a) a literature review;
(b) a study of losses associated with
commercially available 'closed' pipe
junctions;
(c) an experimental study, using hydraulic
models, to investigate the magnitude of
losses at 'open' pit structures.
A theoretical analysis was developed for closed pipe
junctions. The theory was found to be adequate when
checked against available experimental data. For pit
junction structures, the experimental programme comprised
thirty models covering an extensive range of geometric and
hydraulic variables. The model studies indicated that
maximum hydraulic efficiency is attained when the
junction branch point is located on the downstream
face of the pit. Data have been plotted for bend
deflections angles of between 0° and 90°, and for
upstream to downstream pipe diameter ratios within
the range 0.55 to 1.00. Grate inlet flow and submergence
have been identified as parameters affecting
losses. Semi-empirical equations have been developed
to account for junction losses when the branch point
is located on the downstream face of the pit.
Nomenclature
The symbols used in this thesis are listed hereunder.
Alphabetical subscripts have been used which conform to a
standard format. The subscript 'u' refers to the primary
upstream pipe. If more than one upstream pipe converges
at a junction, the second such pipe is characterized by
the subscript 'b' (branch or lateral pipe). The outfall
pipe is identified by the subscript '0'.
Notation
a spacer length for compound mitre bend junction.
Ab mean cross sectional area of the lateral pipe.
Am mean cross section area of the model pipeline.
Ao mean cross sectional area of the outfall pipe.
Ap mean cross sectional area of the prototype pipeline.
Ar model-prototype area ratio.
Au mean eros's sectional area of the upstream pipe.
B pit dimension (square in plan).
Cb dimensionless total energy loss coefficient as defined
by the difference between the lateral total energy line
elevation and the downstream total energy line elevation
when extrapolated linearly to the branch point of the
junction, divided by the average downstream velocity head.
Cu dimensionless total energy loss coefficient as defined
by the difference between the upstream total energy line
elevation and the downstream total energy line elevation
when extrapolated linearly to the branch point of the
junction, divided by the average downstream velocity head.
Db mean diameter of the lateral pipe.
Dm mean diameter of the model pipeline.
Do mean diameter of the outfall pipe.
Dp mean diameter of the prototype pipeline.
Dr model-prototype diameter ratio.
Fo Froude number in the outfall pipe.
g acceleration due to gravity (9.81 m/s2 ).
HGL Hydraulic Grade Line (or pressure line or piezometric
head line).
kb dimensionless pressure head change coefficient as
defined by the difference between the lateral and
downstream pressure line elevations when extrapolated
linearly to the branch point of the junction,
divided by the average downstream velocity head.
ku dimensionless pressure head change coefficient as
defined by the difference between the upstream and
downstream pressure line elevations when extrapolated
linearly to the branch point of the junction, divided
by the average downstream velocity head.
kw dimensionless pressure head change coefficient as
defined by the difference between the water surface
elevation in a pit junction and the elevation of the
downstream pressure line when extrapolated linearly to
the branch point of the junction, divided by the average
downstream velocity head.
Lm characteristic length in a model.
Lp characteristic iength in a prototype.
Lr scalar ratio of the model equal to the characteristic
length of the model divided by the characteristic
length of the prototype.
Pb static pressure in the lateral conduit.
Po static pressure in the main conduit.
Pu static pressure in the upstream conduit.
Qb mean discharge in the lateral pipe.
Qg mean grate flow discharge through the pit grate inlet
~ mean discharge in the model pipeline.
Qo mean discharge in the outfall pipe.
Qp mean discharge in the prototype pipeline.
Qr model-prototype discharge ratio.
Qu mean discharge in the upstream pipe.
R resultant force component acting at the junction
x
used in the impulse-momentum equation.
S depth of water in a pit junction measured from pit
invert elevation to water surface elevation (submergence).
TEL Total Energy Line.
Vb mean velocity in the lateral pipe.
Vm mean velocity in the model pipeline.
Vo mean velocity in the outfall pipe.
Vp mean velocity in the prototype pipeline.
Vr characteristic model-prototype velocity ratio.
Vu mean velocity in the upstream pipe.
pressure head change defining the difference between
the water surface elevation in a junction pit and the
elevation of the downstream pressure line when extrapolated
linearly to the branch point of the junction.
specific weight of a fluid.
H available head.
Hb total energy loss across a junction as defined by the
difference between the lateral total energy line
elevation and the downstream total energy line elevation
when extrapolated linearly to the branch point of the junction.
Hu total energy loss across a junction as defined by the
difference between the upstream total energy line
elevation and the downstream total energy line
elevation when 'extrapolated linearly to the branch
point of the junction.
kp incremental pressure head change coefficient due to
presence of a pit structure, over and above a
theoretical solution
ks incremental pressure head change coefficient due s
to submergence effects, over and above a theoretical
solution .
P/Y change in pressure head as defined by the difference
between an upstream pressure line elevation and the
downstream pressure line elevation when extrapolated
linearly to the branch point of the junction.
p density of water (~ 1000 kg/m3 ).
ab angle of lateral pipe deflection.
eu angle of upstream pipe deflection.

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