Card 7 / 41: Which of the following expresses Reynolds' transport theorem?
A)
The volume integral of the derivative of a scalar or vector field over a time-dependent volume is equal to the volume integral of the velocity of the field plus the surface integral of the product of the outward boundary speed and the field.
B)
The derivative of the volume integral of a scalar or vector field over a time-dependent volume is equal to the volume integral of the derivative of the field plus the surface integral of the product of the outward boundary speed and the field.
C)
The derivative of the volume integral of a scalar or vector field over a time-dependent volume is equal to the volume integral of the derivative of the divergence of the field plus the surface integral of the product of the outward boundary speed and the field.
D)
The derivative of the volume integral of a scalar or vector field over a time-dependent volume is equal to the volume integral of the derivative of the field plus the volume integral of the product of the outward boundary speed and the field.
Answer:
B) The derivative of the volume integral of a scalar or vector field over a time-dependent volume is equal to the volume integral of the derivative of the field plus the surface integral of the product of the outward boundary speed and the field.
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