Fluid FlowBERNOULLI’S EQUATIONMultiplying all terms in Equation 3-10 by the factor g_{c}/mg results in the form of Bernoulli’sequation shown by Equation 3-11.(3-11)z_{1}v^{2}12gP_{1n1}g_{c}gz_{2}v^{2}22gP_{2n2}g_{c}gHeadSince the units for all the different forms of energy in Equation 3-11 are measured in units ofdistance, these terms are sometimes referred to as "heads" (pressure head, velocity head, andelevation head). The term head is used by engineers in reference to pressure. It is a referenceto the height, typically in feet, of a column of water that a given pressure will support. Each ofthe energies possessed by a fluid can be expressed in terms of head. The elevation headrepresents the potential energy of a fluid due to its elevation above a reference level. Thevelocity head represents the kinetic energy of the fluid. It is the height in feet that a flowingfluid would rise in a column if all of its kinetic energy were converted to potential energy. Thepressure head represents the flow energy of a column of fluid whose weight is equivalent to thepressure of the fluid.The sum of the elevation head, velocity head, and pressure head of a fluid is called the totalhead. Thus, Bernoulli’s equation states that the total head of the fluid is constant.EnergyConversionsinFluidSystemsBernoulli’s equation makes it easy to examine how energy transfers take place among elevationhead, velocity head, and pressure head. It is possible to examine individual components of pipingsystems and determine what fluid properties are varying and how the energy balance is affected.If a pipe containing an ideal fluid undergoes a gradual expansion in diameter, the continuityequation tells us that as the diameter and flow area get bigger, the flow velocity must decreaseto maintain the same mass flow rate. Since the outlet velocity is less than the inlet velocity, thevelocity head of the flow must decrease from the inlet to the outlet. If the pipe lies horizontal,there is no change in elevation head; therefore, the decrease in velocity head must becompensated for by an increase in pressure head. Since we are considering an ideal fluid thatis incompressible, the specific volume of the fluid will not change. The only way that thepressure head for an incompressible fluid can increase is for the pressure to increase. So theBernoulli equation indicates that a decrease in flow velocity in a horizontal pipe will result in anincrease in pressure.If a constant diameter pipe containing an ideal fluid undergoes a decrease in elevation, the samenet effect results, but for different reasons. In this case the flow velocity and the velocity headmust be constant to satisfy the mass continuity equation.Rev. 0 Page 23 HT-03

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