Venturi flow meter

1. Venturi flow meter: description

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 Amp�rem�tre series. Finally recorder connected to the regulator Proportinnellement move the needle to the value F value or I.