vC I 2 Vo (2-2)
(a b)2
[z (-b .a)]2
where x [-], is a defined a proportionality constant that depends on the shape of the
PSFM body and the locations of the two openings, points 1 and 2. Once the velocity at
these points is known, the static pressures at these points can be determined using
Bernoulli's equation
p + = -.(p 2) (V -v2 (2-3)
pg 2g pg 2g pg 2g
where p [M/LT2] is the static pressure, vl and v2 [L/T] are local velocities on the PSFM
surface at openings 1 and 2, respectively, p [M/L3] is the density of water, and g [L/T2] is
gravitational acceleration (Klammler et al., 2004). Eqs. (2-2) and (2-3) are then
combined to yield water flux (velocity) Vo [L/T]
o = 2- --2 (2-4)
0 2 X12
where vo is determined by the static pressure differences an location of points 1 and 2.
Based on this, a known head difference between any two points may be used to
calculate the stream velocity around the device if X is known. Using the equations above,
and known x values, the velocity may be estimated for different head differences
depending on the shape and location of the openings, as shown in Figure 2-2. This
figure displays estimated velocities for a range of head differences based on real x values
used for the PSFM devices tested in this study.