A fluid conductor(such as water, for example), carries charges
(positives or electrons). We assume that the fluid formed by
circular slices (or plates) of diameter D travelling at a speed v.
Between the times t and t + dt, one of these slices crosses the distance
x = v dt. The corresponding surface dS = D vdt cuts the magnetic field B.
In this case, according to the Farady law of induction, an electromotive force
rises between the ends of the diameter. Its expression is:
E = dΦ/dt = d(B S)/dt = B dS/dt = B D v dt/dt = BDv
E = B D v
The values of B and D are set. Once E is measured, we ca calculate the value of
the speed of the fluid v = E/BD
v (m/s), T (Tesla), D(m) and E(V)
As the volume flux F is equal to dV/dt = S v dt /dt = S v , we can
measure this flux when we have the value of the speed of the fluid.
F = S v or F = SE/BD
Using the expression of the surface S = π D2/4, we can write:
F = SE/BD = π D2E/4BD = π DE/4B
The SI unit for magnetic field is the Tesla (Newton x second)/(Coulomb x meter).
The smaller magnetic field unit is the Gauss (1 Gauss = 10 x 10 - 4 Tesla).
2. Measurements:
For example:
D = 10 cm = 10 x 10 - 2 m, B = 0.01 Tesla. If a voltmeter as a device of
mesure indicates for E = 3 mVolts, then the related flux has the following measure:
F = π x 10 x 10 - 2 x 3 x 10 - 3 / 4 x 0.01 = 0.0235.
The unit of the flux F is [F]= meter x Volts/Tesla = meter x Volts x Coulomb x meter/Newton x second
Energie (Work) = Newton x meter = Volts x Coulomb. Then:
[F] = meter x Newton x meter x meter/Newton x second = meter 3/second
F = 0.0235 m 3/second
Finally, with = 1 m 3 = 1000 liters; the value of the related flux is:
F = 23.50 liters/second.
