A sensor needs to be installed in a location where the velocity equals the average velocity of the whole cross-sectional area of a blood vessel. Also, the average velocity needs to be determined.

The velocity function v(r) = [P / (4μl)] (R² - r²) is continuous on the interval [0, R], The mean Value Theorem for Integrals says there is a number R_a in [0, R] such that

Solve for R_a from the above equation gives

      R_a = 0.5774R = 0.5774(0.08 x 10^-3)
          = 0.0462 mm  

The average velocity equals the velocity at r = R_a.

      v_ave = v(0.0462 x 10^-3) = P/(4μl)(R² - R_ar²)
            = 400/(4(10 x 10^-3)(20 x 10^-3))((0.08 x 10^-3)²
               - (0.0462 x 10^-3))
            = 2.132 mm/s

The average velocity is 2.132 mm/s and the sensor can be installed at 0.0462 mm from the center.