Continuity Equation (Kinematics and Dynamics of Flow Part-2)

When a fluid is moving, it moves such like that its mass remains conserved.

Let us take a stream through which fluid is flowing. According to continuity equation, mass flow rate remains constant

For section A-A’ mass is given by

Similarly for Section B-B’ 

By contunity equation mass flow rate at both sections should be same, so

“Av” is known as discharge Q

Contunity Equation in 3D

Contunity eqaution will be 

If flow is steady, ∂ρ/∂t = 0

(always remember for steady state ∂/∂t = 0)

Contunity Equation becomes:

If fluid is incompressible then ρ = constant

contunity equation will become

Above equations can be modified according to the conditions given to us in our problems.

Velocity of fluid particle

Let Vr is the resultant velocity of any particle in ant flow. Let u,v,w be the velocity components in x,y,z direction respectively. Then resultant velociy will be 

Acceleration of fluid particle

Let ax,ay,az are the acceleration in x,y,z, directions respectively

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