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I'm in need of a equation that can tell me how much energy/work I need to move an object inside a low air-pressure tube. The equation should (if possible) include drag, object velocity and mass. If there isn't such a equation i would also be happy if you could show me a way how to get to the calculate the work/energy needed.

Thank you for you're time. If you have any questions about my issue please do ask.

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  • $\begingroup$ At high Reynolds number, the drag force is usually modeled as: $F_D=\frac12 \rho v^2 C_A A$ $\endgroup$ – Gert Jan 22 '19 at 17:03
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Assume that the object is moving in the opposite direction to that of the drag force.

If you know the magnitude of the drag force $F_{\rm drag}(t)$ and the speed of the object $v(t)$ then rate at which energy is being dissipated at a particular time $t$ is $F_{\rm drag}(t) \,v(t) $.

To evaluate the total energy dissipation from time $t_{\rm start}$ to time $t_{\rm finish}$ you will need to do an integration $\displaystyle \int_{t_{\rm start}}^{t_{\rm finish}} F_{\rm drag}(t) \,v(t) \, dt$

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  • $\begingroup$ Assume that the object is moving in the opposite direction to that of the drag force. Assume? Friction (here air drag) is ALWAYS in the opposite direction of motion. $\endgroup$ – Gert Jan 22 '19 at 16:58
  • $\begingroup$ @Gert I do not know why I wrote that sentence but on reflection you can have a moving fluid applying a frictional force on an object in the direction of motion of the object when the object is moving slower than the fluid. $\endgroup$ – Farcher Jan 22 '19 at 23:56

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