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ESE Civil 2016 Paper 2: Official Paper

Option 4 : 96 rpm

CT 3: Building Materials

2962

10 Questions
20 Marks
12 Mins

The equation of parabolic profile is given by:

\(Z = \frac{{{\omega ^2}{r^2}}}{{2g}}\)

For point A: (0.2, y); \(y = \frac{{{{\rm{\omega }}^2}{{\left( {0.2} \right)}^2}}}{{2{\rm{g}}}}\)

For point B: (0.45, d + y + 0.5); \(d + y + 0.5 = \frac{{{{\rm{\omega }}^2}{{\left( {0.45} \right)}^2}}}{{2{\rm{g}}}}\)

Or

\(d + y = \frac{{{{\rm{\omega }}^2}{{\left( {0.45} \right)}^2}}}{{2{\rm{g}}}} - 0.5\)

By Volume Conservation:

Volume of fluid before rotation = Volume of fluid after rotation

i.e. V_{1} = V_{2}

V_{1} = π (0.45)^{2} d

V_{2} = π (0.45)^{2}(d + 0.5) - 1/2 {π(0.45)^{2}(d + y + 0.5) - π (0.2)^{2}y}

Now, V_{1} = V_{2}

On solving we get,

d + y = 0.5 + 16y/81

From above equation 1 and 2, substitute the values of ‘d + y’ and ‘y’ in equation no 3.

\(\frac{{{{\rm{\omega }}^2}{{\left( {0.45} \right)}^2}}}{{2{\rm{g}}}} - 0.5 = 0.5 + \frac{{16}}{{81}}\left( {\frac{{{{\rm{\omega }}^2}{{\left( {0.2} \right)}^2}}}{{2{\rm{g}}}}} \right)\)

**We get ω = 10 rad/sec**

We know that

\(\omega = \frac{{2\pi N}}{{60}}\;or\;N = \frac{{60\omega }}{{2\pi }}\)

Or

\(N = \frac{{60 \times 10}}{{2\pi }}\) = 96 rpm