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Formula of the day

tau = T * r / J
Torsional Shear Stress

When you twist a shaft, shear stress develops inside it. The stress is zero at the center and maximum at the surface. It equals the torque times the radius, divided by the polar moment of inertia. For example, a thin-walled tube can carry almost as much torque as a solid shaft of the same weight because the material is all near the surface where it is most effective. It is used to design drive shafts, axles, and couplings.

Mechanical Engineering
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Geology & Earth Science/ Seismology

Peak Ground Acceleration Attenuation (Simplified)

Published Jul 11, 2026 Updated Oct 22, 2026

PGA = a * 10^(b*M) / (R+c)^d

Geology & Earth Science/ Seismology

Tsunami Wave Speed (Shallow Water Wave)

Published Jul 11, 2026 Updated Oct 22, 2026

v = sqrt(g*h)

Geology & Earth Science/ Seismology

Fault Slip Rate

Published Jul 11, 2026 Updated Oct 22, 2026

Slip Rate = Total Displacement / Time Elapsed

Geology & Earth Science/ Seismology

Seismic Moment

Published Jul 11, 2026 Updated Oct 22, 2026

M0 = μ * A * D

Geology & Earth Science/ Seismology

Moment Magnitude Scale

Published Jul 11, 2026 Updated Oct 22, 2026

Mw = (2/3)*log10(M0) - 10.7

Geology & Earth Science/ Hydrogeology

Darcy's Law (Groundwater Flow Velocity)

Published Jul 11, 2026 Updated Oct 22, 2026

v = -K * (dh/dl)

Geology & Earth Science/ Hydrogeology

Groundwater Volumetric Flow Rate (Darcy's Law)

Published Jul 11, 2026 Updated Oct 22, 2026

Q = K * A * (dh/dl)

Geology & Earth Science/ Hydrogeology

Hydraulic Conductivity from Intrinsic Permeability

Published Jul 11, 2026 Updated Oct 22, 2026

K = (k * ρ * g) / μ

Geology & Earth Science/ Hydrogeology

Well Drawdown (Thiem Equation, Confined Aquifer)

Published Jul 11, 2026 Updated Oct 22, 2026

s = (Q / (2π*T)) * ln(R/r)

Geology & Earth Science/ Hydrogeology

Aquifer Storativity (Confined Aquifer)

Published Jul 11, 2026 Updated Oct 22, 2026

S = Ss * b

Geology & Earth Science/ Hydrogeology

Specific Yield (Unconfined Aquifer)

Published Jul 11, 2026 Updated Oct 22, 2026

Sy = Volume of Water Drained / Total Volume of Aquifer

Geology & Earth Science/ Hydrogeology

Porosity

Published Jul 11, 2026 Updated Oct 22, 2026

n = (Vv / Vt) * 100

Geology & Earth Science/ Hydrogeology

Groundwater Recharge Rate

Published Jul 11, 2026 Updated Oct 22, 2026

R = P - ET - RO

Geology & Earth Science/ Hydrogeology

Well Specific Capacity

Published Jul 11, 2026 Updated Oct 22, 2026

Sc = Q / s

Geology & Earth Science/ Hydrogeology

Groundwater Seepage (Linear) Velocity

Published Jul 11, 2026 Updated Oct 22, 2026

v_s = v / n

Geology & Earth Science/ Hydrogeology

Stream Discharge

Published Jul 11, 2026 Updated Oct 22, 2026

Q = V * A

Geology & Earth Science/ Hydrogeology

Stream Gradient

Published Jul 11, 2026 Updated Oct 22, 2026

Gradient = Elevation Drop / Stream Length

Geology & Earth Science/ Seismology

Rock/Mineral Density (Specific Gravity)

Published Jul 11, 2026 Updated Oct 22, 2026

SG = Density of Sample / Density of Water

Geology & Earth Science/ Hydrogeology

Gravimetric Soil Moisture Content

Published Jul 11, 2026 Updated Oct 22, 2026

w (%) = ((Mass_wet - Mass_dry) / Mass_dry) * 100

Geology & Earth Science/ Hydrogeology

Drainage Basin Relief Ratio

Published Jul 11, 2026 Updated Oct 22, 2026

Rh = Relief / Basin Length

Geology & Earth Science/ Hydrogeology

Flood Recurrence Interval (Weibull Formula)

Published Jul 11, 2026 Updated Oct 22, 2026

T = (n+1) / m

Biology/ Genetics

Hardy-Weinberg Equilibrium

Published Jul 8, 2026 Updated Oct 22, 2026

p² + 2pq + q² = 1

Biology/ Genetics

Punnett Square Ratio (Monohybrid)

Published Jul 8, 2026 Updated Oct 22, 2026

Genotype ratio = 1:2:1

Biology/ Population Ecology

Logistic Population Growth

Published Jul 8, 2026 Updated Oct 22, 2026

dN/dt = rN(1 − N/K)

Biology/ Population Ecology

Michaelis-Menten Kinetics

Published Jul 8, 2026 Updated Oct 22, 2026

v = V_max[S] / (K_m + [S])