Question
Download Solution PDFThe continuity equation is based on which of the following applications?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Continuity equation:
\(\begin{array}{l} \frac{{\partial \left( {\rho u} \right)}}{{\partial x}} + \frac{{\partial \left( {\rho v} \right)}}{{\partial y}} + \frac{{\partial \left( {\rho w} \right)}}{{\partial z}} + \frac{{\partial \rho }}{{\partial t}} = 0\\ \frac{{\partial \rho }}{{\partial t}} + \bar V.\left( {\rho \vec V} \right) = 0 \end{array}\)
Continuity equation:
The continuity equation is the equation of conservation of mass in a fluid flow.
According to the law of conservation of mass:
Rate of flow in section 1 - 1 = Rate of flow at section 2 - 2
\({\rho _1} \times {A_1} \times {V_1} = {\rho _2} \times {A_2} \times {V_2}\)
For Incompressible fluids
\( {A_1} \times {V_1} = {A_2} \times {V_2}\)
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