BERNOULLI’S EQUATION Fluid Flowwhere:Q = heat (Btu)U = internal energy (Btu)PE = potential energy (ft-lbf)KE = kinetic energy (ft-lbf)P = pressure (lbf/ft^{2})V = volume (ft^{3})W = work (ft-lbf)SimplifiedBernoulliEquationBernoulli’s equation results from the application of the general energy equation and the first lawof thermodynamics to a steady flow system in which no work is done on or by the fluid, no heatis transferred to or from the fluid, and no change occurs in the internal energy (i.e., notemperature change) of the fluid. Under these conditions, the general energy equation issimplified to Equation 3-9.(PE + KE + PV)_{1} = (PE + KE + PV)_{2}(3-9)Substituting appropriate expressions for the potential energy and kinetic energy, Equation 3-9 canbe rewritten as Equation 3-10.(3-10)mgz_{1}g_{c}mv^{2}12g_{c}P_{1}V_{1}mgz_{2}g_{c}mv^{2}22g_{c}P_{2}V_{2}where:m = mass (lbm)z = height above reference (ft)v = average velocity (ft/sec)g = acceleration due to gravity (32.17 ft/sec^{2})g_{c} = gravitational constant, (32.17 ft-lbm/lbf-sec^{2})Note: The factor g_{c} is only required when the English System of measurement is used and massis measured in pound mass. It is essentially a conversion factor needed to allow the unitsto come out directly. No factor is necessary if mass is measured in slugs or if the metricsystem of measurement is used.Each term in Equation 3-10 represents a form of energy possessed by a moving fluid (potential,kinetic, and pressure related energies). In essence, the equation physically represents a balanceof the KE, PE, PV energies so that if one form of energy increases, one or more of the otherswill decrease to compensate and vice versa.HT-03 Page 22 Rev. 0

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