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Fluids Equations

QuestionAnswer
Bernoulli's P + 0.5*p*v**2 + p*g*h = Ptot
Mass Flow mdot = p*v*A
Cantilever Beam Stress m*c/I
Cantilever Beam Deformation F*L**3 / 3*E*I
Second Moment of Area I, equations vary from shape to shape for squares b*h**3 / 12
Conservation of Mass and Momentum mdot*vi - mdot*vf = delta Momentumn = Pi*Ai - Pf*Af
Conservation of Energy pf*hTf*vf*Af - pi*hTi*vi*Ai = dQ/dt + Wdot
Dynamic Pressure 0.5*p*v**2 = q = gamma*p*M**2 /2 = kenetic energy per volume
Hydraulic Head P/p*g + v**2 / 2*g + Z = Ptot/p*g = Head
H - Enthalpy Total working energy in a fluid
Specific Heat Need Youtube video
Speed of sound a = sqrt(gamma*R*T) = sqrt(gamma*P/p)
Pressure and Density Relation in an ideal gas isentropic flow P/p**gamma = const = P0/p0**gamma
Stagnation Temperature Ratio Relations P/P0 = (p/p0)**gamma = (T/T0) ** (gamma/(gamma-1))
Reynold's Number p*v*D/mew
Laminar Flow Re <= 2100
Turbulent Flow Re >= 2100
RTT dBsys/dt = dBCV/dt - Bin + Bout (B is any value)
Discharge Coefficient Cd = mdot/(A*sqrt(2*p*(P2-P1)))
Flow Coefficient Cv = Q*sqrt(SG/dP), SG- Specific Gravity for water is 1
Area Mach Relation dA/A = (M**2 - 1)dv/v
Pressure Loss in Laminar Flow (Darcy Weiback) dP = f * (L/D) * 0.5*p*v**2
Mass Spring Natural Frequency (massless spring) w = sqrt(K/m)/2*pi (Hz) = sqrt(K/m) (rad/s)
Mass Spring Natural Frequency (Massive spring) w = sqrt(K/m+ms/3)/2*pi
Work Energy = int(fdx)
Spring Energy Es = 1/2 kx**2
Internal Energy U = mCvT
Enthalpy h = mCpT
Euler's Buckling Equation n*pi**2 * E * I / L**2
n in Euler's Buckling Equation pinned-pinned: 1 pinned-fixed: 2 fixed-fixed: 4 fixed-free:0.25
Torque Equation T = I*alpha
Bolt Preload Equation T = F*K*e(minor diameter)
Von Mises Stress Equation sig = sq((sig1-sig2)^2 + (sig2-sig3)^2 + (sig3-sig1)^2)
Single Pin Shear Tav(Average Shear Stress) = V/Apin T
Bolt Stress
Created by: user-1980122
 

 



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