Data Analysis

3.7.1 Combined sewer overflows

Site surveys had to be carried out because the drawings obtained from Design & Building Services were design drawings and not as-built drawings. Consequently, there were discrepancies between some of the dimensions given on the drawings and

the actual site measurements. The actual overflow chamber, weir and pipe

dimensions were measured on site. By finding the distances between manhole

invert level, determination of the length and fall of the relevant pipes was possible. The data was then used to establish the extent of backing up in the sewerage system during an overflow event and to determine the storage in the chamber and the upstream pipes.

At low flows, when the inflow is equal to the continuation flow, there is a continuous relationship between depth and discharge. As the flow increases and the throttle pipe starts to control upstream depths, the continuation flow is related to the depth of water in the overflow chamber which determines the depth of flow in the inlet pipe. The continuity equation controls the relationship between the inlet depth and the continuation flow, i.e.

Flow In - Flow Out = Rate of Change in Storage (3.1)

According to Lonsdale et al, (1993) the change in storage in the time step n to n+1 is given in finite difference form by:

(Qin„ + Q i n J j - (Qout„ + QoutnJ j = Snt1 - S„ (3.2)

where Q = flow rate

S = Storage Volume dt = Time Step

Where the continuation flow and spill flow are both measured, the values may be added together to give Qout at any time step. Any missing data in the inflow can then be calculated by rearranging Equation 3.2.

Qin„+1 = Qout„ + Qoutw1 + (S„t1 - S„) - Qin„ (3.3)

Missing continuation flow values can be determined using data from the inflow monitor and storage volumes calculated from the inflow depth measurement.

Qout„+i = Q|nn + Qinw1 + (S„

The continuation flow is a function of the differential head across the throttle pipe. As described by Lonsdale et al (1995), the results of the block-off test detailed in 3.6.1 can be used to relate the differential head across the throttle pipe to the continuation flow. The continuation flow at any time can be calculated from the known depths either side of the previous time step, the inflow and the storage in the chamber, using

equation 3.1. In practice, the time-depth curve is generally not smooth and a

theoretical curve is fitted based on an energy analysis of the flow (Lonsdale et al, 1995). The discharge.through the throttle pipe is determined by applying the energy equation:

Datum

Vi

h, + — + z = h. + — + losses (3.5)

1 2g 4 2g v '

Losses are made up of an entry loss, 0.5v22 /2 g , a friction head loss, ;Uv32 /2gd , and an exit loss, (v3 - v4)2 /2g .

A form of the Manning equation which relates X directly to the roughness of the

1 1

X = 0.180k3 / d 3 (3.6)

Where k = surface roughness (m)

d = pipe diameter (m)

In most cases v1 is small compared to the other velocities. Where no throttle plate or penstock is fitted to the throttle pipe v2 = v3 and as a first approximation, v4 is proportional to v3 so that v4 = Cv3. Rearranging equation 3.5 gives:

Q = CdA ^ j h 7 (3.7)

Where A = cross-sectional area of throttle pipe

h0 = drop in hydraulic gradient across throttle pipe Cd = coefficient of discharge, and is given by

C_ = _'d 1

(1-C)2 + 0.5 + 0.180Lk3 /d 3 1 4

Values of C and k are found by producing the best fit curve from the blocking-off test data.

The following expression was used to obtain any missing data from the spill flow monitors:

Q = c d |V 2 g BH3 (3.8)

Where Cd = coefficient of discharge B = Breadth of weir

H = Head above weir crest

The large storage capacity of the upstream system of the Extended stilling pond overflow meant that a blocking-off test developed by Lonsdale et al (1995) was impractical because of the length of time required to fill and empty the overflow chamber. Consequently a calibration curve for the spill pipe was produced. This was

done by plotting the values of discharge and depth for the spill pipe onto a log scale to produce a straight line relationship. The method of least squares was then used to

find the line of best fit for the raw data. The equation of the straight line was then

determined and translated back to a power law relationship between depth and

discharge:

Q o c D n (3.9)

Where Q = Spill Discharge (m3/sec) D = Depth in Spill Pipe (m) n = constant

Q = k D n (3.10)

Where k = constant

Taking logs of both sides gives a straight line relationship (y = c + mx):

log Q = log k + n log D (3.11)

The constants k and n are found by calculating the gradient of the line and the y- intercept.

Several rainstorm events had missing velocity readings for the spill flow, but the calibration curve enabled estimates to be made of these values, thus providing a set of complete data.

The efficiency of the screens was calculated for total gross solids and for individually classified materials, e.g. sanitary towels, paper towels, tampons, etc.. The efficiency definitions used were as follows:

Efficiency of screen = mass of gross solids retained by screen x 100 % (3.12)

total mass of gross solids presented to screen

Efficiency of screen for individual materials

mass of material retained by screen

x 100 % (3-13)

3.7.2 Sewage treatment works

Drawings were unavailable for Long Lane sewage treatment works so a full survey of the works inlet was carried out and a working drawing produced. Manual calibration checks were made during each site visit and the monitor was checked at the end of

each testing period to ensure the data collected were reliable. The data were

downloaded and transferred on to a personal computer in the same way as the CSO field data. The raw depth and velocity values were then loaded from SSAS into a spreadsheet to calculate the flowrates through the screens. The relationship between the depth readings and the velocity readings was plotted for several test days to check there was consistency in the data. The data chosen for these plots were randomly selected. For each individual test the mean flowrate through the screen was found. The efficiency definitions used for the combined sewer overflows were used to find the screen retention efficiencies of the two screens at the sewage treatment works.