The mathematical expression for the above law is stated as mt 0 where m mass of

The mathematical expression for the above law is

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The mathematical expression for the above law is stated as: ∆m/∆t = 0 , where m = mass of the system 11
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LAW OF CONSERVATION OF MASS The inflows, outflows and change in storage of mass in a system must be in balance. The mass flow in and out of a control volume (through a physical or virtual boundary) can for an limited increment of time be expressed as: dM = ρ i v i A i dt - ρ o v o A o dt ….. [1] where dM = change of storage mass in the system (kg) ρ = density (kg/m 3 ) v = speed (m/s) A = area (m 2 ) dt = an increment of time (s) If the outflow is higher then the inflow - the change of mass dM is negative -the mass of the system decreases And obvious - the mass in a system increase if the inflow is higher than the outflow. The Law of Mass Conservation is a fundament in fluid mechanics and a basis for the Equation of Continuity and the Bernoulli Equation . 12
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LAW OF CONSERVATION OF MASS Example Q. Water with density 1000 kg/m 3 flows into a tank through a pipe of 50 mm inside diameter. The velocity in the pipe is 2 m/s . The water flows out of the tank through a pipe with inside diameter 30 mm with a velocity of 2.5 m/s . Using equation (1) the change in the tank content after 20 minutes can calculated as: dM = (1000 kg/m 3 ) (2 m/s) (3.14 (0.05 m) 2 / 4) ((20 min) (60 s/min)) - (1000 kg/m 3 ) (2.5 m/s) (3.14 (0.03 m) 2 / 4) ((20 min) (60 s/min)) Ans. = 2590.5 kg 13
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THE EQUATION OF CONTINUITY The Law of Conservation of Mass states that mass can be neither created or destroyed. Using the Mass Conservation Law on a steady flow process - flow where the flow rate do not change over time - through a control volume where the stored mass in the control volume do not change - implements that inflow equals outflow This statement is called the Equation of Continuity.
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  • Fall '18
  • amjad naseer

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