Conservation of Mass

Volumetric Flow Rate

Continuity Equation - h1012v3_33

Thermodynamics Heat Transfer and Fluid Flow Volume 3 of 3
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CONTINUITY EQUATION Fluid Flow Replacing in Equation 3-2 with the appropriate terms from Equation 3-1 allows the direct V calculation of the mass flow rate. (3-3) m r A v Example: The water in the pipe of the previous example had a density of 62.44 lbm/ft³. Calculate the mass flow rate. Solution: m r V m _(62.44lbm ft³ ) (1.22 ft³ sec ) m 76.2^lbm sec Conservation of Mass In thermodynamics, you learned that energy can neither be created nor destroyed, only changed in form. The same is true for mass. Conservation of mass is a principle of engineering that states that all mass flow rates into a control volume are equal to all mass flow rates out of the control volume plus the rate of change of mass within the control volume. This principle is expressed mathematically by Equation 3-4. (3-4) m_in m_out Dm Dt where: = the increase or decrease of the mass within the control volume over a Dm Dt (specified time period) Steady-State Flow Steady-state flow refers to the condition where the fluid properties at any single point in the system do not change over time. These fluid properties include temperature, pressure, and velocity. One of the most significant properties that is constant in a steady-state flow system is the system mass flow rate. This means that there is no accumulation of mass within any component in the system. HT-03 Page 10 Rev. 0

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