2013-3-6 Conservation of Mass Principle Total mass entering Total mass leaving Net change in mass the CV during△t 、the CV during△i, （within the CV during△r 1in-1mout=△11cy mn=50kg min -mou dmcv/dt =风=20 Conservation of mass :30 kg principle for a bathtub Mass Rate Balance Conservation of mass principle time rate offlow control volume me inleti at timet exit e at timet Dashed line >Or in symbols me (Eq.4a) dt where Mass Rate Balance for a CV ri is the mass flow rate=amount of mass flowing through a cross section per unit time Dot over symbol denotes the time rate of change 4-6 3 2013-3-6 3 Conservation of Mass Principle Conservation of mass principle for a bathtub Mass Rate Balance 4-6 time rate of change of mass contained within the control volume at time t time rate of flow of mass in across inlet i at time t time rate of flow of mass out across exit e at time t mi me dt dm = & − & cv (Eq. 4a) Mass Rate Balance for a CV where is the mass flow rate = amount of mass flowing through a cross section per unit time m& Dot over symbol denotes the time rate of change Conservation of mass principle ¾ Or in symbols