Final answer:
Mass flow rate is a physics concept involving the amount of mass flowing through a given cross-sectional area of a pipe. It is calculated using the product of fluid density, area, and velocity, and remains constant throughout a pipe's length for an incompressible fluid
Step-by-step explanation:
Understanding Mass Flow Rate in Fluid Dynamics
The concept described in the student's question pertains to mass flow rate in fluid dynamics, a subfield of Physics. Mass flow rate is the rate at which mass passes through a cross-sectional area of a pipe in a given time interval Δt. It is calculated as the product of the fluid's density (ρ), the cross-sectional area (A), and the average velocity (ŭ) of the fluid through the pipe. Using the equation ρAx = m for a segment of pipe of length x, the mass flow rate is given by Q = ρAu, where Q denotes the volume flow rate.
Considering an incompressible fluid flowing through a pipe that changes in diameter, the flow rate must remain consistent, thus resulting in varied velocities at different cross-sectional areas. A larger cross-sectional area at the inlet (A1) yields a slower velocity (v1), while a smaller cross-sectional area at the outlet (A2) leads to a higher velocity (v2). This inverse relationship ensures the continuity of flow for the incompressible fluid.
To further illustrate, the mass flow rate in both sections must be equal by the principle of conservation of mass. Therefore, adjustments in the fluid's velocity correspond proportionally to changes in the cross-sectional area, maintaining the mass flow rate as a constant throughout the pipe's length.