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The Law of Mass Conservation states that

• "mass can neither be created nor destroyed"

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/m³)

v = speed (m/s)

A = area (m²)

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.

Example - 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 (0.05 m)²/4) (20 min 60 s/min)

                - (1000 kg/m³)(2.5 m/s)(3.14 (0.03 m)²/4)(20 min 60 s/min)

    = 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
• 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
• Technical Terms in Fluid Mechanics - Some of the most common used technical terms used in fluid mechanics