Question

In an analysis of fragmented blast muck, the mean fragment size is found to be 60 cm with uniformity index of 1.25. Considering Rosin-Ramler equation, the cumulative mass fraction, in percent, to pass the grizzly screen size of 100 cm is \(\underline{\hspace{1cm}}\). (round off to 2 decimal places)

Hint:

The Rosin-Ramler equation is useful in predicting particle size distribution and can help estimate the mass fraction passing a given sieve.

Answer 1

Correct Answer: 71

The Rosin-Ramler equation is given by:
\[ F(x) = 1 - \left(\frac{x}{x_{\text{50}}}\right)^{n} \] where \( x \) is the fragment size, \( x_{\text{50}} \) is the mean size, and \( n \) is the uniformity index.
Given: \( x_{\text{50}} = 60 \, \text{cm} \), \( n = 1.25 \), and \( x = 100 \, \text{cm} \).
Substitute the values into the equation:
\[ F(100) = 1 - \left(\frac{100}{60}\right)^{1.25} \] \[ F(100) = 1 - (1.6667)^{1.25} \approx 1 - 2.0109 = 0.0109 \] Thus, the cumulative mass fraction is:
\[ F(100) \times 100 = 0.0109 \times 100 = 1.09% \] Rounded to two decimal places:
\[ \boxed{1.09%} \]