Velocity, pressure and other properties like cross-section of fluid flow are the functions of time. If these fluid properties do not change w.r.t time, it is called steady flow.

Mathematically, steady flow equations can be written as-

Let V be the velocity of fluid particles

a be the acceleration of fluid particles

We know that,

V ⃗ = V (S ⃗)

a ⃗ = a (S ⃗)

So, steady flow equation w.r.t. time changes can be given by-

[∂V/∂t](x0, y0, z0)    =    0

[∂P/∂t](x0, y0, z0)    =    0

[∂ρ/∂t](x0, y0, z0)    =    0

Where,

P = Pressure of fluid flow

ρ = Density of fluid

x0 = Initial component of x

y0 = Initial component of y

z0= Initial component of z

If Velocity, pressure and other fluid properties change w.r.t time, it is called unsteady flow.

Mathematically, unsteady flow equations can be written as-

[∂V/∂t](x0, y0, z0)    ≠    0

[∂P/∂t](x0, y0, z0)    ≠    0

[∂ρ/∂t](x0, y0, z0)    ≠    0

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