Fluid Mechanics and Conservation of Mass

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

The Law of Mass Conservation states that"a 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 inn 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 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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