HYD-00 · laboratory
Manning, Darcy–Weisbach, weirs, hydraulic jump and gradually varied flow.
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27 governing sheets
Uniform-flow discharge Q = (1/n) A R^{2/3} S^{1/2} (SI).
Open channelFrictional head hf = f (L/D) V² /(2g).
Pipe flowV = C √(R S) for uniform open-channel flow.
Open channelQ = (2/3) Cd L √(2g) H^{3/2} for a sharp-crested weir.
WeirsSequent depth y2/y1 = ½ (−1 + √(1+8 Fr₁²)).
Rapidly varied flowQ = A1 V1 = A2 V2 for incompressible flow.
ContinuitySI form V = 0.849 C R^{0.63} S^{0.54}.
Pipe flowQ = Cd A √(2 g H) through a small orifice.
OrificesQ = k i A. Discharge through a porous prism, i = Δh/L.
SeepageQ = C L H^{3/2}. Sharp-crested weir; C absorbs Cd √(2g) and end contractions.
WeirsQ = Cd A √(2 g h). A hole in a tank, vena contracta inside Cd.
Orificesy2/y1 = ½ (−1 + √(1+8 Fr1²)). Momentum across a rapid jump.
Open channeldy/dx = (S0 − Sf) / (1 − Fr²). Backwater when Fr < 1 and Sf ≠ S0.
Open channelV = C √(R S). Ancestor of Manning; C ≈ R^{1/6}/n.
Open channelV = 0.849 C R^{0.63} S^{0.54} (SI). Water-works pipe formula.
Pipe flowQ2/Q1 = n2/n1, H2/H1 = (n2/n1)², P2/P1 = (n2/n1)³ at constant diameter.
PumpsE = y + q²/(2 g y²) for a rectangular channel. Minimum at critical depth.
Open channelFr = v/√(g y), yc = (q²/g)^{1/3} for a rectangle. Critical when Fr = 1.
Open channelv = √(2 g h). Ideal speed of a free jet under head h.
OrificesQ = 1.84 (L − 0.1 n H) H^{3/2} (SI). End contractions n = 0, 1 or 2.
WeirsQ = Cd A √(2 g (H − y/2)). Inlet-control orifice when the barrel is unsubmerged at the outlet.
Culverts1/√f = −1.8 log10[(ε/D/3.7)^{1.11} + 6.9/Re]. Explicit Haaland fit to Colebrook.
Pipe flowf = 64/Re if Re < 2300, else Haaland. A two-regime Moody snapshot.
Pipe flowhf = Σ fi (Li/Di) V²/(2g) with Q the same, Vi = Q / Ai.
Pipe flowQ = A V. The definition of mean velocity in a prismatic reach.
Open channelQ = (1/n) A R^{2/3} S^{1/2}. Uniform open-channel flow.
Open channelhf = f (L/D) V² / (2g). The pipe friction equation.
Pipe flow