Final answer:
The question involves calculating the mass flow rate in a pipe with laminar flow using the parabolic velocity distribution, integrating over the cross-sectional area while considering fluid density and velocity.
Step-by-step explanation:
The student's question pertains to the measurement of the mass flow rate of a fluid in laminar flow through a circular pipe using a hot-wire velocity meter. This involves the understanding of fluid dynamics, including the velocity distribution, which is indicated to be parabolic. The relationship among velocity, cross-sectional area, and mass flow rate is crucial, as the mass of fluid entering the pipe equals the mass exiting the pipe, due to the principle of continuity.
The key to calculating the mass flow rate is integrating the velocity profile over the pipe's cross-section, considering fluid properties like density and viscosity.
To calculate the mass flow rate when the velocity distribution is parabolic, one would use the density of the fluid (p), the cross-sectional area (A), and the velocity at different radii (u). The equation of continuity, Poiseuille's law, and the relation Q = Au, where Q is the flow rate and u is the average velocity, are fundamental concepts required to solve such problems.