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The effect of fluid flow on the free vibration and instability of fluid-conveying single-walled carbon nanotubes is studied. The possibility of developing a technique to measure the mass flow rate of fluid is examined. Atomistic simulations and the continuum beam model are used. Simulations are performed to quantify the inertial, stiffness, Coriolis, and centrifugal forces generated by flow during the free vibration. A numerical expression is developed to measure the mass flow rate of the fluid velocities up to 40% of the critical flow velocity. This observation is useful to quantify the mass flow measurement of fluid conveying single-walled carbon nanotubes.