Fluid FlowCONTINUITY EQUATIONContinuityEquationThe continuity equation is simply a mathematical expression of the principle of conservation ofmass. For a control volume that has a single inlet and a single outlet, the principle ofconservation of mass states that, for steady-state flow, the mass flow rate into the volume mustequal the mass flow rate out. The continuity equation for this situation is expressed by Equation3-5.(3-5)m_{inlet}m_{outlet}(rAv)_{inlet}= (rAv)_{outlet}For a control volume with multiple inlets and outlets, the principle of conservation of massrequires that the sum of the mass flow rates into the control volume equal the sum of the massflow rates out of the control volume. The continuity equation for this more general situation isexpressed by Equation 3-6.(3-6)m_{inlets}m_{outlets}One of the simplest applications of the continuity equation is determining the change in fluidvelocity due to an expansion or contraction in the diameter of a pipe.Example: Continuity Equation - Piping ExpansionSteady-state flow exists in a pipe that undergoes a gradual expansion from a diameter of6 in. to a diameter of 8 in. The density of the fluid in the pipe is constant at 60.8 lbm/ft^{3}.If the flow velocity is 22.4 ft/sec in the 6 in. section, what is the flow velocity in the 8in. section?Solution:From the continuity equation we know that the mass flow rate in the 6 in. section mustequal the mass flow rate in the 8 in. section. Letting the subscript 1 represent the 6 in.section and 2 represent the 8 in. section we have the following.Rev. 0 Page 11 HT-03

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