Fluid Flow BERNOULLI’S EQUATIONRestrictionsontheSimplifiedBernoulliEquationPractical applications of the simplified Bernoulli Equation to real piping systems is not possibledue to two restrictions. One serious restriction of the Bernoulli equation in its present form isthat no fluid friction is allowed in solving piping problems. Therefore, Equation 3-10 onlyapplies to ideal fluids. However, in reality, the total head possessed by the fluid cannot betransferred completely from one point to another because of friction. Taking these losses of headinto account would provide a much more accurate description of what takes place physically.This is especially true because one purpose of a pump in a fluid system is to overcome the lossesin pressure due to pipe friction.The second restriction on Bernoulli’s equation is that no work is allowed to be done on or by thefluid. This restriction prevents two points in a fluid stream from being analyzed if a pump existsbetween the two points. Since most flow systems include pumps, this is a significant limitation.Fortunately, the simplified Bernoulli equation can be modified in a manner that satisfactorilydeals with both head losses and pump work.ExtendedBernoulliThe Bernoulli equation can be modified to take into account gains and losses of head. Theresulting equation, referred to as the Extended Bernoulli equation, is very useful in solving mostfluid flow problems. In fact, the Extended Bernoulli equation is probably used more than anyother fluid flow equation. Equation 3-12 is one form of the Extended Bernoulli equation.(3-12)z_{1}v^{2}12gP_{1n1}g_{c}gH_{p}z_{2}v^{2}22gP_{2n2}g_{c}gH_{f}where:z = height above reference level (ft)v = average velocity of fluid (ft/sec)P = pressure of fluid (lbf/ft^{2})n= specific volume of fluid (ft^{3}/lbm)H_{p}= head added by pump (ft)H_{f}= head loss due to fluid friction (ft)g = acceleration due to gravity (ft/sec^{2})The head loss due to fluid friction (H_{f}) represents the energy used in overcoming friction causedby the walls of the pipe. Although it represents a loss of energy from the standpoint of fluidflow, it does not normally represent a significant loss of total energy of the fluid. It also doesnot violate the law of conservation of energy since the head loss due to friction results in anequivalent increase in the internal energy (u) of the fluid. These losses are greatest as the fluidflows through entrances, exits, pumps, valves, fittings, and any other piping with rough innersurfaces.Rev. 0 Page 25 HT-03