Formula solvers — J

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Jacob Distance-Drawdown Transmissivity

T = \frac{2.303 \, Q}{2 \pi (s_1 - s_2)} \log_{10}\!\frac{r_2}{r_1}

Water & WastewaterTransmissivity from two observation wells read at the same instant during a constant-rate pumping test. Subtracting one Cooper-Jacob drawdown from the other cancels the storage term entirely, which is why this is the direction that can actually be solved for T.

Jakob Number

\mathrm{Ja} = \frac{c_p \, \Delta T}{h_{fg}}

Heat TransferSensible heat against latent heat: how much of the energy crossing a boiling or condensing surface goes into changing the fluid's temperature rather than changing its phase. Small in almost every practical case, which is what makes phase change such an efficient way to move heat.

Jar Test Dose Scale-Up

D = \frac{V_{st} \, C_{st}}{V_{s}}

Water & WastewaterWater TreatmentChemistryConverts millilitres of stock solution added to a jar test beaker into the equivalent plant dose in mg/L of raw water.

JMAK (Avrami) Transformed Fraction

X = 1 - \exp\!\left( -k \, t^{\,n} \right)

Metallurgy & Heat TreatmentThe S-shaped curve every isothermal transformation follows: slow while nuclei are still appearing, fast while they grow into free space, slow again as they run into each other. Avrami wrote it in 1939, Johnson and Mehl the same year, and it is the arithmetic behind every TTT diagram and every recrystallisation anneal.

Joint Stiffness Ratio of a Bolted Joint

C = \frac{k_{b}}{k_{b} + k_{m}}

Machine DesignThe share of an external load that lands on the bolt rather than on the clamped members, set by the two stiffnesses in parallel. Usually between 0.1 and 0.3, and the reason a properly preloaded bolt barely notices the load it is holding.

Junction Temperature from Power and Thermal Resistance

T_j = T_a + P R_{\theta JA}

Semiconductors & ChipsHow hot the silicon gets: ambient temperature plus the power dissipated multiplied by the thermal resistance from junction to air. It is Ohm's law with temperature for voltage, watts for current, and K/W for ohms.