Physical significance of substantial time derivative
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The substantial derivative (or total derivative) is defined as the time rate of change of a fluid property of a fluid element as it travels through a given flow field (velocity field). It is denoted by
D/Dt=∂/∂t + (q·grad)
where q is the velocity field vector and grad denotes gradient.
∂/∂t is the local derivative - the time rate of change at a fixed point.
q·grad is the convective derivative - the time rate of change due to the movement of a fluid element through a flow field whose properties are spatially different (i.e., over here it's 20° Celsius; over there it's 25°).
In somewhat more palatable form,
D/Dt=∂/∂t + u*∂/∂x + v*∂/∂y + w*∂/∂z
where u, v, and w are the x, y, and z components of velocity vector q.
hope so help u
D/Dt=∂/∂t + (q·grad)
where q is the velocity field vector and grad denotes gradient.
∂/∂t is the local derivative - the time rate of change at a fixed point.
q·grad is the convective derivative - the time rate of change due to the movement of a fluid element through a flow field whose properties are spatially different (i.e., over here it's 20° Celsius; over there it's 25°).
In somewhat more palatable form,
D/Dt=∂/∂t + u*∂/∂x + v*∂/∂y + w*∂/∂z
where u, v, and w are the x, y, and z components of velocity vector q.
hope so help u
Answered by
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D/Dt=∂/∂t + (q·grad)
where q is the velocity field vector and grad denotes gradient.
∂/∂t is the local derivative - the time rate of change at a fixed point.
q·grad is the convective derivative - the time rate of change due to the movement of a fluid element through a flow field whose properties are spatially different (i.e., over here it's 20° Celsius; over there it's 25°).
In somewhat more palatable form,
D/Dt=∂/∂t + u*∂/∂x + v*∂/∂y + w*∂/∂z
where u, v, and w are the x, y, and z components of velocity vector q.
where q is the velocity field vector and grad denotes gradient.
∂/∂t is the local derivative - the time rate of change at a fixed point.
q·grad is the convective derivative - the time rate of change due to the movement of a fluid element through a flow field whose properties are spatially different (i.e., over here it's 20° Celsius; over there it's 25°).
In somewhat more palatable form,
D/Dt=∂/∂t + u*∂/∂x + v*∂/∂y + w*∂/∂z
where u, v, and w are the x, y, and z components of velocity vector q.
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