Detailed hydraulics articles with formulas, worked examples, FAQs, and keywords — written next to the solvers.
Series adds head at the same flow. Parallel adds flow at the same head. How to intersect a quadratic system curve and when unequal pumps idle.
Discharge is set by the drop between free surfaces, not by the hump. Crown vacuum, priming, practical 7–8 m lift, and the same physics as NPSH.
Elbows, valves, and entrances are not minor on a short suction line. Sum K, convert to L_eq, expansion/contraction, and when a control valve should be Cv.
Diameter is a trade between velocity (erosion, noise, NPSH) and head loss (pumping cost). Typical water velocities, continuity, and how to iterate D.
Capacity is the lesser of what the entrance admits and what the barrel plus tailwater can pass. HW/D limits, Ke, Manning n, and a screening example.
Gravity sewers are open channels inside a circle. A and R from y/D, why peak Q is not at full, self-cleansing velocity, and the rational method.
Fr > 1 can jump to a sequent depth. Bélanger relation, energy dissipation in stilling basins, and how critical depth sits between the two.
Differential-pressure meters infer Q from a constriction. β ratio, Cd, the 1/√(1−β⁴) factor, permanent pressure loss, and ISO 5167 caveats.
If a valve closes faster than 2L/c, you get the full acoustic surge. Celerity, t_c, slow-closure estimate, surge tanks, and column separation.
p/ρg + V²/2g + z is conserved only without friction. How to draw HGL/EGL, add pump head, and fold in Darcy plus minor losses.
Replace a chain or a twin with one pipe that has the same K in h = KQ². Choose L_eq, back-calculate D_eq, and skeletonize a network.
NPSHa is a system number, NPSHr is a pump number. Build the suction energy budget, include fittings K, and see why hot water and altitude eat the margin.
Three tanks, three pipes, one unknown junction head. How to guess the piezometric level, reverse a flow, and why Newton-Raphson beats nested square roots.
Continuity first, then loop head balance. How ΔQ is calculated, a four-pipe worked loop, equivalent pipes, and when to move on to Newton-Raphson.
The Moody diagram is a picture of the Colebrook-White equation. Laminar shortcut, implicit iteration, explicit fits, and a worked Re–ε/D example.
Darcy-Weisbach is the general friction formula. Hazen-Williams is a water-only shortcut. Here is when each one is valid, a worked comparison, and how they connect through f.