Numerical - Range of linear scale - Metrology & Quality Control

Q.  Calculate the range of linear scale for pressure ratios between 0.6 to 0.8. The air is supplied at 5 bar to the control jet, which has a diameter of 0.45 mm and the diameter of measuring jet is 0.83 mm.
k1  = – 0.5 & k2  = 1.1
- Published on 07 Aug 15

a. 0.244 mm
b. 0.0976 mm
c. 0.0244 mm
d. None of the above

ANSWER: 0.0244 mm

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    Discussion

  • Sravanthi   -Posted on 23 Oct 15
    - In a back pressure gauge, air at constant pressure flows through orifices Am and Ac and then flows to the atmosphere. Depending on the two orifices Am and Ac , the relation between pressure of orifices and pressure supplied is obtained.

    - Orifice Am is the measuring orifice.

    - Orifice Ac is the control orifice and has a constant area.


    Given: Range of pressure ratio = 0.6 to 0.8, k = -0.5, k1 = 1.1

    Formula: p2 / p1 = k (Am / Ac) + k1 is the linear relation for the pressure ratios between 0.6 to 0.8.

    Solution:

    Substituting the given values we get,

    1) Ac = (π / 4) x d2 = (π / 4) x 0.452

    = 0.159 mm2

    Similarly, Am = π d t = 2.607 t mm2

    Ratio of Am / Ac = 2.607 t / 0.159 = 16.39 t


    2) Assuming pressure ratio (p2 / p1) = 0.6 and substituting the values in the formula,

    p2 / p1 = k (Am / Ac) + k1

    0.6 = - 0.5 (16.39 t1) + 1.1

    t1 = 0.061 mm

    Similarly, assuming pressure ratio (p2 / p1) = 0.8 and substituting the values in the formula,

    t2 = 0.0366

    Range of linear scale (t) between orifice and workpiece = t1 - t2 = 0.061 – 0.0366 = 0.0244

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