The various considerations involved in the design of grit chambers are as follows: 1. Settling Velocity 2. Surface Overflow Rate (SOR) 3. Detention Period 4. Bottom Scour and Flow through Velocity 5. Velocity Control Devices 6. Number of Units 7. Dimensions of Each Unit 8. Loss of Head.
1. Settling Velocity:
Grit chamber may be designed on a rational basis by considering it as a sedimentation basin. The grit particles are treated as discrete particles settling with their own settling velocities. The settling velocity is governed by the size and specific gravity of the grit particles to be separated and the viscosity of the sewage.
The minimum size of grit to be removed is 0.2 mm although 0.15 mm is preferred for conditions where considerable amount of ash is likely to be carried in the sewage. The specific gravity of girt may be as low as 2.4 but for design purposes a value of 2.65 is used.
The settling velocity of discrete particles can be determined using the appropriate equation depending upon the Reynolds number as indicated below:
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(a) Stokes’ Law:
The settling velocity of discrete particles is given by Stokes’ law as-
(b) Transition law—Hazen’s Equation:
In the range of Reynolds number between 1 and 1000 the nature of settling of particles is neither laminar nor turbulent and hence it is termed as transitional settling of particles.
The settling velocity of grit particles in the transition range is also calculated by the Hazen’s modified equation-
In which T is the temperature of sewage in °C.
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The settling velocity of grit particles in the range of 0.1 mm and 1 mm can be determined using equation 11.8 or its approximate empirical form of equation 11.10 and these should be used in the design of grit chambers which are designed to remove particles of size 0.15 mm or 0.2 mm.
(c) Newton’s Law:
When the particle size increases beyond 1 mm and Reynolds number beyond 1000 the Newton coefficient of drag CD assumes a constant value of 0.4 and by introducing this value of CD in equation 11.6 the following equation is obtained-
Equation 11.11 is known as Newton’s equation which is applicable for particles of size greater than 1 mm and Reynolds number in the range Re > 103 to 104.
ADVERTISEMENTS:
For particles of size greater than 1 mm and Reynolds number in the range Re > 103 to 104 the nature of settling of particle is turbulent and hence it is termed as turbulent settling. Thus equation 11.11 can be used to determine the settling velocity of grit particles in the case of turbulent settling.
2. Surface Overflow Rate (SOR):
Grit chambers are basically settling tanks. The efficiency of an ideal grit chamber or settling tank is expressed as the ratio of the settling velocity (Vs) of the particles to be removed to the surface overflow rate (V0), i.e.,
Table 11.2 gives settling velocities of different size particles of specific gravity 2.65 (inorganic grit particles) and 1.20 (organic matter) and corresponding surface overflow rates for 100% removal of these particles based on equation 11.8.
However, the behaviour of a real grit chamber or settling tank departs significantly from that of the ideal grit chamber or settling tank due to turbulence and short-circuiting resulting from eddy, wind and density currents. Hence the Surface Overflow Rates (SOR) should be diminished to account for the chamber or tank performance. Following equation can be used to determine the SOR for a real grit chamber or settling tank for a given efficiency of grit removal and chamber or tank performance.
The values of n are 1/8, 1/4, 1/2 and 1 for very good, good, poor and very poor performance. It can be seen that the design surface overflow rate will be 66.07%, 60.36%, 50% and 33.33% of the settling velocity of the grit particles to be removed to achieve 75% removal efficiency in grit chamber with very good, good, poor and very poor chamber or tank performance respectively. In practice values of two-thirds to one half are used in design depending upon the type of grit chamber. These values are much higher than those needed for organic solids of specific gravity 1.2.
3. Detention Period:
The detention period for grit chambers may vary from 45 to 90 seconds. A detention period of 60 seconds is usually adopted in the design of grit chambers.
4. Bottom Scour and Flow through Velocity:
The efficiency of grit chamber is very much affected by bottom scour. The scouring process itself determines the optimum velocity of flow through the grit chamber. This may be explained by the fact that there is a critical velocity of flow Vc beyond which particles of a certain size and density once settled may be again set in motion and reintroduced into the stream of flow. The critical velocity for scour may be calculated from modified Shield’s formula-
Where Kc = 3 to 4.5. A value of 4 is usually adopted for grit particles.
For a grit particle size of 0.2 mm, the formula gives critical velocity values of 17.1 to 25.6 cm/s. In actual practice, a horizontal velocity of flow of 15 to 30 cm/s is used at peak flows. The horizontal velocity of flow should be maintained constant at other flow rates also to ensure that only organic solids and not the grit are scoured from the bottom.
5. Velocity Control Devices:
Numerous devices have been designed in an attempt to maintain a constant horizontal velocity of flow through grit chambers in the recommended range of 15 to 30 cm/s. Since none of the control devices designed so far have been able to maintain the velocity at a constant level at all flows, a limit of variance in the velocity of 5-10% above and below the desired velocity of flow is recommended.
A satisfactory method of controlling velocity of flow through grit chambers is by using a control section which when placed at the outlet end of the grit chamber or grit channel, varies the cross- sectional area of flow in direct proportion to the flow.
The control sections commonly used are proportional weirs and Parshall flumes and the same are discussed below:
(a) Proportional Flow Weir:
A proportional flow weir is a combination of a weir and an orifice. It consists of a rectangular plate with an opening with curved sides for flow to pass through. The shape of the opening of the proportional flow weir is such that the discharge through the weir is proportional to the depth of flow over the weir crest.
Thus it maintains a nearly constant velocity of flow in the grit chamber or grit channel at different flows by varying the depth and hence the cross-sectional area of flow. As such proportional flow weir may be used as a control section for a grit chamber of rectangular cross-section. As indicated below the sides of the proportional flow weir are so curved that the width of the opening decreases as the square root of the increasing depth of flow over the weir crest.
In general the discharge over a rectangular weir is given by
Q = K l H3/2 … (11.14)
In which
Q = discharge;
l = width of weir opening.
H = depth of flow over the weir crest; and
K = a constant
Equation 11.14 may be expressed as-
Q = K (lH1/2)H … (11.14a)
From equation 11.14(a) it is evident that if (lH1/2) is made constant the depth H will vary directly with discharge. Thus for different values of H, the corresponding values of the width I can be determined and hence the curved shape of the sides of the weir can be determined. It may, however, be noted that for the curve obtained by the relationship lH1/2 = constant, as H → 0, l → ∞, which means that the width of the weir opening becomes infinity at the crest.
The infinity tending profile is however not practicable. As such in order to overcome this practical limitation Sutro modified the shape of the weir profile so that a finite width at the weir crest may be provided. The proportional flow weir profile as given by Sutro is shown in Fig. 11.10, which has its sides diverging downward in the form of hyperbolic curves having the equation-
In which a and b are respectively the height and width of the small rectangular shaped opening which forms the base of the weir.
The discharge through this weir is given by-
Where Q = discharge;
Cd = coefficient of discharge;
b = base width of the weir;
H = depth of flow over the crest; and
a = dimension of weir
The coefficient of discharge Cd for such weirs varies from 0.60 to 0.65 and is usually taken as 0.61. The dimension a of the weir is usually assumed between 25 mm and 50 mm, with a suggested value of 35 mm.
The proportional flow weir should be set 100 to 300 mm above the bottom of grit chamber to provide for grit storage or for operation of mechanical devices for cleaning of grit chamber. The weir should also be set at such as elevation as to produce a free fall into the outlet channel as it cannot function under submerged conditions. Each grit chamber should be provided with a separate control weir.
(b) Parshall Flume:
A Parshall flume is an open constricted channel which can be used both as a measuring device and also as a velocity control device, more commonly used for the later purpose in grit chamber. The flume has a distinct advantage over the proportional flow weir, as it involves negligible head loss and can work under submerged conditions up to certain limits.
The limits of submergence are 50% in case of 150 mm throat width and 70% for wider throat widths upto 1 m. Another advantage is that one control section can be installed for 2 to 3 grit chambers. The flume is also self-cleansing and there is no problem of clogging. As the Parshall flume is a rectangular control section the grit chamber above it must be designed to approach a parabolic cross-section to maintain a constant velocity of flow at all discharges.
To maintain a constant velocity of flow in the grit chamber at all discharges the cross-sectional area of the chamber should change in direct proportion to the change in the discharge. Thus we have-
The parabolic section may be approximated to a rectangular section with a trapezoidal bottom. Hence grit chambers or grit channels of rectangular section with trapezoidal bottom may be used with a Parshall flume.
In such a case the variations in velocity at maximum and minimum flow conditions from the designed velocity of flow should be within permissible limits as given by the following equations:
Where Q = rate of flow (in lps);
Qmin = minimum rate of low (in lps);
Qmax = maximum rate of flow (in lps);
W = throat width (in m);
HA = depth of flow in upstream leg oi me flume at one-third point (in m);
Z = a constant (in m);
D = depth of flow in grit chamber (in m);
B = width of grit chamber (in m); and
V = velocity of flow (in m/s) at a particular depth of flow
Recommended throat widths for different ranges of flow along with the dimensions of the various elements of the Parshall flume for the different throat widths are given in Table 11.3 which should be strictly adhered to.
6. Number of Units:
In case of manually cleaned grit chambers at least two units should be provided. All mechanically cleaned grit chambers should be provided with a manually cleaned grit chamber to act as a bypass.
7. Dimensions of Each Unit:
The surface areas required for each unit is worked out on the basis of the surface overflow rate chosen. The breadth of tank is fixed with reference to the control device adopted. The length is then worked out on the basis of the selected surface overflow rate.
In case of mechanically cleaned grit chambers the horizontal dimension may be readjusted to suit the standard sizes of the mechanical equipment after ensuring that the flow-through velocity is within the prescribed limits. The depth of flow is determined by the horizontal velocity and the peak flow.
Additional depth for storage of grit between intervals of cleaning should be provided in case of intermittent cleaning. A freeboard of 150 to 300 mm should be provided. Bottom slopes are based on the type of scraper mechanism used.
8. Loss of Head:
Loss of head in a grit chamber varies from 0.06 to 0.6 m depending on the device adopted for velocity control.