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Tony's Intertwingled Memex • Reference Manual

Flow Control Valve Restriction (Civil & Environmental Engineering)

Formulas & Definitions

A water resources engineer designs an automated municipal overflow valve for a storm runoff conduit. The flow discharge velocity factor V(x)V(x)V(x) (in m/s\text{m/s}m/s) through the throttle orifice is modeled as a function of the aperture opening width xxx (in centimeters) by:

V(x)=x2−5x+6x−3V(x) = \frac{x^2 - 5x + 6}{x - 3}V(x)=x−3x2−5x+6​

During valve tuning, the aperture is calibrated around the critical transition setting x=3 cmx = 3\text{ cm}x=3 cm.

  1. Explain why direct evaluation at x=3 cmx = 3\text{ cm}x=3 cm fails.
  2. Apply an algebraic factoring strategy to find the limiting flow velocity lim⁡x→3V(x)\lim_{x\to 3} V(x)limx→3​V(x).