# Fluid Flow and Bernoulli Equation

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Flow characteristics of gasesSection 2.4.2: “Momentum changes in a fluid” in Chemical Engineering vol. 1,Coulson and Richardson, Elsevier, Oxford, 6th ed. 2013.Consider a fluid flowing through an inclined pipe, see fig. 25.Figure 25. Fluid flowing through an inclined pipeThe mechanical energy balance between two points (1 and 2) in the fluid (ie in Joules kg-1) can be represented as:P1/+ z1g + V12/21 = P2/+ z2g + V22/22 + FWhere: is the density of the fluid in kg m-3, P is the pressure (Nm-2), z the height above level (m), g the acceleration due to gravity (9.8 m s-2), V the average velocity (m s-1), F losses due to friction and a correction factor = 0.5 for laminar flow and 1.0 for turbulent flow. Assuming a horizontal pipe (z1 = z2), turbulent flow and negligible friction loss:P1/+ V12/2 = P2/+ V22/2This is the simplified Bernoulli equation, which can be represented as:P/+ V2/2 = constantP/is the “pressure energy” and V2/2 is the kinetic energy, both in J kg-1.The Bernoulli equation can be expressed as:(P2 – P1)/= (V22 - V12)/2If a fluid is made to pass into a narrower section of pipe (i.e. from one of cross sectional area A1 to another of area A2) at a steady mass flow rate, then the velocity of the fluid must increase because it is squeezed. Conservation of mass i.e. mass in = mass out:

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