Conservation of Mass (Continuity Equation):

The continuity equations is a conversation of mass equation for fluid flow. Fluid mass must always be conserved in fluid systems. This holds true for pipes, channels, and various other systems. The idea is that the mass into a system cannot disappear along the way, and an equal amount of mass must exit the system:

m_1 = m_2

where:

  • m = mass

or when applied to fluid flow,

Q_1 = Q_2

ρ_1A_1v_1 = ρ_2A_2v_2

where:

  • ρ = density or mass density (kg/m3, slugs/ft3)
  • A = cross-sectional area of the flow (m2, ft2)
  • V = velocity of the flow (ft/sec)

and normally you can assume the fluid is incompressible so ρ12 therefore:
Because liquids can be assumed to have constant density over fairly large vertical distances, the continuity equation simplifies to:

The most common form of the continuity equation is:

A_1v_1 = A_2v_2

where:

  • Q = discharge (ft3/sec)
  • A = cross-sectional area of the flow (ft2)
  • V = velocity of the flow (ft/sec)

Note: These equations will work as long as you keep your units straight. That way you can use either SI or US as long as you keep everything in order.


Other Variations of the Continuity Equation:


Solve for Flow:

Q=Av
Solve for the Area of Flow:
A={Q\over v}
Solve for the velocity of the Fluid:
v={Q\over A}

References:

  1. To be inserted.

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