Fluid Mechanics and Conservation of Mass

The law of conservation of mass states that mass can neither be created or destroyed

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The Law of Mass Conservation states that"a mass can neither be created nor destroyed".

law of mass conservation

The inflows, outflows and change in storage of mass in a system - must be in balance.

The mass flow inn and out of a control volume (through a physical or virtual boundary) can for an limited increment of time be expressed as:

dM = ρi vi Ai dt - ρo vo Ao dt (1)

where

dM = change of storage mass in the system (kg)

ρ = density (kg/m3)

v = speed (m/s)

A = area (m2)

dt = an increment of time (s)

If the outflow is higher then the inflow - the change in mass dM is negative - and the mass in the system decreases. And obvious - the mass in a system increases if 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.

Example - The Law of Mass Conservation

Water with density 1000 kg/m3 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/m3)(2 m/s)(3,14 x 0.05 (m) x 0.05 (m) / 4)(20 x 60 s) - (1000 kg/m3)(2.5 m/s)(3.14 x 0.03 (m) x 0.03 (m) / 4)(20 x 60 s)

    = 2590.5 kg

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Related Topics

  • Fluid Mechanics The study of fluids - liquids and gases. Involves various properties of the fluid, such as velocity, pressure, density and temperature, as functions of space and time.

Related Documents

  • Equation of Continuity The Equation of Continuity is a statement of mass conservation
  • Technical Terms in Fluid Mechanics Some of the most common used technical terms used in fluid mechanics
  • Equations in Fluid Mechanics Common fluid mechanics equations - Bernoulli, conservation of energy, conservation of mass, pressure, Navier-Stokes, ideal gas law, Euler equations, Laplace equations, Darcy-Weisbach Equation and more

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