The Venturi floe meter determines flowrate through a pipe.
Through the device, the mass of the passing fluid is conserved,
especially for the Upstream and downstream on both sides of
the throat orifice element; that is: m1 = m2. According to the relationships:
m1 = ρ1 V1, and m2= ρ2 V2
We assume that the density of the liquid is constant; the derivative gives:
dm1/dt = dm2/dt, that is
ρ2 dV2/dt = ρ2 dV2/dt
V is the volume and ρ is the density.
F = dV/dt is the flow of the fluid.
Let's write:
F1 = F2 = F (1)
Or:
dV1/dt = dV2/dt that gives : S1dx1/dt = S2 dx2/dt then:
v1S1 = v2S2 (2)
v is the speed of the fluid and S is the surface of the tube where the
fluid passes.
The surface area of the tube is S1 = πD2/4; the area of the
throat element is S2 = πd2/4
The Bernoulli Theorem gives:
Pt1 = Pt1,
Ps1 + Pd1 = Ps2 + Pd2
where Pt is the total pressure, Ps static pressure, and Pd
dynamic pressure. Hence:
Ps1 - Ps2 = Pd2 - Pd1
or:
Ps1 + v12/2g + 0 = Ps2 + v22/2g + 0
D'o:
Ps1 - Ps2 = v22/2g - v12/2g (3)
The static pressure difference ΔP = Ps1 - Ps2 is determined
by the the equation:
ΔP = ρ g h; (4)
where ρ is the density
of the liquid in the U tube, g is the gravity, and h is the depth of the
liquid (as a mecury element Hg) in the U tube.
Finally, the equatio (3) becomes:
ρ g h = [v22 - v12]/2g (5)
From the relationship (1) and (2), we can write:
ρ g h = = [(F/S2)2 - (F/S1)2]/2g =
F2 [(1/S2)2 - (1/S1)2]/2g.
That yields::
F2 = 2 ρ g2 h /[(1/S2)2 - (1/S1)2] (6)
We define the constant Cst:
Cst = 2 ρ g2 /[(1/S2)2 - (1/S1)2]
To have:
F2 = Cst h
Hence:
F = [Cst . h]1/2 (7)
For each value of the depth h, we have a value of the flow rate.
2. Measurements
A DPCell (cell differential pressure)
Plugged in Ps1 and Ps2 play exactly the same role.
Of course, the value of the height h translud the regulator
Is received by it in the form of:
H = F2/Cst.
The governor multiplies that value by the constant
Cst and then extract its square root (sqrt). It Impose
Therefore (via a rheostat for example) a current
I insit of electric in his circuit containing a
Ampremtre series. Finally recorder connected to the regulator
Proportinnellement move the needle to the value
F value or I.
