Page 130 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Screening 85

5.4.2.1 Mathematical Relationships The variables that affect Q(screen) are (Wahl and
From Figure 5.7a, the screen is installed on an inclined plane Einhellig, 2000)
(about 608 recommended) just below an ‘‘acceleration plate.’’
The flow balance, seen from the drawing, is Dq(screen) ¼ F, s, w, f, u, H, screen arc radius (5:4)
¼ Cs[2gH] 0:5 (5:5)
Q(inflow) ¼ Q(screen) þ Q(bypass) (5:2)

where
and the flow through the screen is
F is the Froude number (dimensionless)
H is the specific energy at a given slot location (m)
Q(screen) ¼ v(screen) A(screen) (5:3) C is the discharge coefficient (dimensionless)
3
q(screen) is the flow per unit width of screen (m =s=m)
where
3
Q(inflow) is the inflow of raw water to screen (m =s) The discharge coefficient (two are lumped here to simplify
Q(screen) is the raw water flow passing through the screen the discussion) is dependent on F and the geometric variables,
3
(m =s) with relationships given by Wahl (2001) from experimental
Q(bypass) is the raw water flow passing over the screen data and computations. Since F changes along the length of
3
surface and leaving (m =s) the screen, Q(screen) must be computed slot by slot and
v(screen) is the apparent velocity of raw water through the summed.
screen (m=s) A less accurate but easier-to-apply approach to determine
2
A(screen) is the total area screen surface (m ) v(screen) is to use a relationship from empirical data as given
by Wahl (1995, p. 5) for specific conditions, i.e., for an arc
Other variables, seen in Figure 5.7b, are: the width of the screen, w ¼ 1.52 mm, s ¼ 1.0 mm, i.e.,
wire, w, the slot opening, s, the angle of inclination of
the screen, u, and the inclination of the plane of the top wire v(screen) ¼ a þ b q (5:6)
surface with respect to the plane of the screen, f; the flow
through a single slot opening is DQ. To clarify the definition
where
of A(screen), if the number of wire elements is n(wire elem-
a ¼ intercept of experimental curve (m=s)
ents) and if the width of the screen is w(screen), then
¼ 0.71 m=s for data of Wahl (1995, p. 4)
A(screen) ¼ w(screen) n(wire elements) (s þ w).
b ¼ slope of experimental curve (dimensionless)
¼ 1.83 for data of Wahl (1995, p. 5)
5.4.2.2 Theory 3
q ¼ specific flow to screen (m =s=m screen width)
As stated by Wahl (1995, p. 2), each V-shaped wire is tilted at
an angle, f 58, giving a tilt so that the upstream edge is
Equation 5.6 provides an estimate of v(screen) for the stated
offset to the flow, as shown in Figure 5.7b. A thin layer of
conditions. For a screen with s ¼ 0.5 mm, v(screen) is reduced
the flow is thus sheared off at the bottom, which means, at the
about 18% (Wahl, 2001, p. 13). [Wahl’s data were given in
same time, that there is no boundary layer and hence no
terms of q (flow per unit width of screen) for an arc
friction. The mechanical shearing action of the leading edge
screen of length 0.457 m (1.5 ft); v(screen) was calculated
of each of the tilted wires is enhanced by the Coanda effect
as v(screen) ¼ q=w(screen).]
(after Henri-Marie Coanda who observed the phenomenon in
1910), which is the tendency of a fluid jet to remain, attached
to a solid boundary. 5.4.2.3 Design
Due to this effect, which is prevalent at supercritical Table 5.3 summarizes data from Wahl (2001) as may be
velocities, the flow remains attached to the top surface of a useful for an initial estimation of design variables, such as
given upstream wire and is directed to hit the face of the sizing the screen, setting the angle, u, determining the total
next downstream wire (Wahl and Einhellig, 2000, p. 3). head drop, and in selecting a fabric. The steep angle, u,
For subcritical velocity, v(slot) is calculated by the orifice serves two purposes: (1) to cause supercritical velocity, i.e.,
equation, i.e., is proportional to the square root of the depth F 1, and (2) to, in turn, have a velocity high enough to
of water above the slot. Thus, a portion of the flow is ensure that the screen is self-cleaning. The maximum prac-
directed down through the slot opening of width, s. The tical screen dimension (one piece) is 2.4 5.5 m (8 18 ft);
incremental discharge, DQ, through each opening is a func- screens are usually fabricated, however, in smaller sections
tion of the flow velocity and the thickness of the sheared and bolted together (Hydroscreen, 2002). Also the screens
water layer. The velocity over the screen depends, in turn, on are usually designed to accommodate the required flow
the elevation drop from the crest of the acceleration plate to and existing conditions of available head and installation
the screen. footprint size.