Level & analytical formulas

Open tank, high side to the tank, low side to atmosphere; $h$ is the liquid height above the tapping point. If the transmitter sits a height $h_0$ below the tapping point (impulse line full of the same liquid), $\Delta P=\rho g(h+h_0)$, and the transmitter is given a zero suppression of $\rho g{h}_0$ so that empty still reads 4 mA.

$A$ is the displacer's uniform cross-sectional area and $h$ the submerged length (partly submerged); the buoyancy of the vapour above the liquid is neglected. Apparent weight $=W-A\rho gh$, where $W$ is the displacer's weight in air.

Insulating liquid, $0\le h\le L$, gas above the liquid taken as ${\epsilon }_r=1$, end (fringing) effects neglected. Capacitance is linear in $h$; at $h=0$ it is the empty value $2\pi {\epsilon }_{0}L/\ln (b/a)$.

$t$ is the round-trip time and $v$ the wave speed in the space above the liquid: speed of sound for ultrasonic, speed of light for radar.

$R=8.314$ J/(mol K), $F=96485$ C/mol, $T$ in kelvin. $E_0$ is the potential at pH 0 and combines the reference and internal potentials. An ideal electrode with its isopotential point at pH 7 and zero offset gives $E=S(7-\mathrm{pH})$, that is, 0 mV at pH 7.

$T$ in kelvin. At 25 °C ($298.15$ K) the slope is about 59.16 mV per pH; at 0 °C about 54.2 mV; at 50 °C about 64.1 mV.

$K$ in m${}^{-1}$, $R$ the measured cell resistance in ohms, $\kappa$ in S/m. Unit conversion: 1 S/m $=10^4\mu$S/cm.

Steady, fully developed laminar flow of a Newtonian liquid in a tube of radius $r$ and length $L$ under pressure drop $\Delta P$; $Q$ is the volume flow rate.

Sphere radius $r$ and density ${\rho }_s$ falling at constant terminal speed $v_t$ in an unbounded Newtonian liquid of density ${\rho }_f$; valid for small Reynolds number (${\rho }_f{v}_t(2r)/\mu$ below about 1, creeping flow). Near a container wall the sphere falls slower, so a wall correction is needed.