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Equation Sheet - EQUATION SHEET Hydrostatics constant...

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Unformatted text preview: EQUATION SHEET Hydrostatics, constant density: Hydrostatic panel force: F = thGA, Yer: ’InSina/(hooA). ch= -lxysin01(hco.4) CV mass: d/ddfcvpdv) + EOJAV)out — 20$th = 0 CV angular momentum: d/dt(‘|'CV p(l'o xV)a‘v) + EPAV(r0xv)oul_ EPAVU'oXth: 2M0 p2 - p1= -y(22-21). 7 = 93 Buoyant force: F 3 = yflmwisplaced volume) CV momentum: d/dt( In dev) + EWAVWLu. - 2[(PAV)v]in = 2F Steady flow energy: (pl'y+aV2/2g+z)in = Acceleration: dV/dr = aV/a: (p/‘y+aV2/2g+z)°m + hm“, - hm + hm + u(6V/6x) + v(6V/6)') + w(aV/az) Incompressible stream function ¢I(x,y): Velocity potential ¢(x.y.z): u= Bill/8y; v = -6¢/ax u = (ht/ax: v = (Malay; w = awe: Turbulent friction factor: 1/ W = -2.0 103,0[3/(37d) + 2.51/(Red\/f)] Bernoulli unsteady irrotational flow: aqb/a: + Idp/p + v2/2 +g. = Const = flL/dwz/(zg) where f = Moody chart friction factor Orifice, nozzle. venturi flow: Q=C4A.hmtE2Ap/{p(1—a‘)}]"z. B = d/D Laminar flat plate flow: 5/x = 5.0/Rel’2, Turbulent flat plate flow: 8/x = 0.16/Rex , c, = 0.664/Rei’2, CD = l.328/Re,'_’2 c, = 0.027/Rey’, CD = 0.03I/Rez” Isentropic flow: TolT= l +{(k-1)/2}Ma2, One»dimensional isentropic area change: Po/P = (To/ow“ ”. mm = (To/n“— " A/A*=(I/Ma)n+uk— l)/2}Ma2]“’2""+”""") Prandtl-Meyer expansion: K = (k+1)/(k-l), w=K""tan'1[(Ma2—l)/K]m-tan"(Ma2-l)m Gradually varied channel flow: dy/dx = (50 - S)/(1 — Frz). Fr = wvcm Pipe head loss: It, Uniform flow. Manning‘s n, SI units: Vo(m/S) = (1.0/n)[Rhtrrofnstl’2 Euler turbine formula: Power = pQ(u2V,2 - uan), u = no ...
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