Rate of flow or Discharge and Continuity equation
Rate of Flow or Discharge (Q):
It is defined as the quantity of fluid flowing per second through a section of pipe or channel. For incompressible fluid or liquid, the rate of flow of discharge is expressed as the volume of fluid flowing across the section per second. For compressible fluid, the rate of flow is usually expressed as the weight of fluid flowing across the section.
Units: For liquids------------- Q= m3/sec. or litres/sec.
For gases --------------------- Q= kgf/sec. or N/sec
Consider a liquid flowing through a pipe in which,
A = Cross- sectional area of the pipe
V = Average velocity of fluid across the section
Then discharge, Q = A x V
Continuity Equation
The equation based on the principle of conservation of mass is called Continuity Equation. For a fluid flowing through a pipe at all cross-section, the quantity of fluid per second is constant. Consider two cross-sections of a pipe as shown
Let v1 = Average velocity at cross- section 1-1
ρ 1 = Density at section 1-1
A1 = Area of pipe at section 1-1
And v2, ρ 2, A2 are the corresponding values at section 2-2
V1 ρ 1 A1 = V2 ρ 2 A2
The above equation is applicable to the compressible as well as in-compressible fluids and is called continuity equation. If the fluid is incompressible, then, ρ 1 = ρ 2 and continuity equation reduce to:
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