BERNOULLI’S EQUATION Fluid FlowSo the decrease in elevation head can only be compensated for by an increase in pressure head.Again, the fluid is incompressible so the increase in pressure head must result in an increase inpressure.Although the Bernoulli equation has several restrictions placed upon it, there are many physicalfluid problems to which it is applied. As in the case of the conservation of mass, the Bernoulliequation may be applied to problems in which more than one flow may enter or leave the systemat the same time. Of particular note is the fact that series and parallel piping system problemsare solved using the Bernoulli equation.Example: Bernoulli’s EquationAssume frictionless flow in a long, horizontal, conical pipe. The diameter is 2.0 ft at oneend and 4.0 ft at the other. The pressure head at the smaller end is 16 ft of water. Ifwater flows through this cone at a rate of 125.6 ft^{3}/sec, find the velocities at the two endsand the pressure head at the larger end.Solution:V_{1}A_{1}v_{1}v_{1}V_{1}A_{1}v_{1}125.6ft^{3}secp(1 ft)2v_{1}40ftsecv_{2}V_{2}A_{2}v_{2}125.6ft^{3}secp(2 ft)2v_{2}10ftsecz_{1}v^{2}12gP_{1n1}g_{c}gz_{2}v^{2}22gP_{2n2}g_{c}gP_{2n2}g_{c}gP_{1n1}g_{c}g(z_{1}z_{2})v^{2}1v^{2}22g16 ft0 ft40ftsec210ftsec22^{}32.17ft lbmlbf sec^{2}39.3 ftHT-03 Page 24 Rev. 0

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