Attempt b and c

Equation Sheet for Question 1 Relative frequency: f;= f(x) y s, = Q(x,)- Q(x,-1) = 5 g(x)dx Cumulative frequency distribution: Q(x) Amount of particles with size s x Amount of all particles dQ(x) Differential frequency distribution: 7(x) = or 9(xi) Q(xi+1)-Q(xi) dx Xi+1-Xi N w.x, Nwx, Weighted mean size: x j=! = N i=1 N Ef.w.x w(x)xqy(x)dx fw, u(x)q,()dx Now , , Nos = i=1 n-th moment of particle size distribution: 4. = {1*= [x"q(v)dx Number weighted mean size: M1/Mo Length weighted mean size: Mz/u1 Surface weighted mean size: uz/uz Volume weighted mean size: M4/M3 Total surface area & volume of all particles (for cube and sphere shapes): S = 3 Nax = aNx*q,(x)dx N i=1 N. Vs = EN,Bx? = BNxq_(x)dx = i=1 Q1. Sample A consists of spherical particles with diameter d. The differential frequency distribution qn (d) (number based) for sample A is as follows: 9n (d) = 0 for ds 75 um qn (d) = 0.008 um? for 75 um 200 pm Sample B consists of needle-shaped particles with circular cross-section of diameter D and length L. The particle diameter D is equal to 10 um, independent of particle length. The cumulative frequency distribution Qn (L) (number based) for the particle length L is as follows: Qn (L) = 0 for Ls 50 um Qn (L) = 0.004 (L-50) for 50 um 500 pm Qn (L) = 1 for L > 500 pm (a) For sample A, calculate the value of the cumulative frequency distribution Qn (d) when d = 90 pm and d = 160 um. [4 marks] (b) Calculate the number weighted average diameter and the volume weighted average diameter of the particles in sample A. [6 marks] (c) For sample B, calculate the differential frequency distribution qn (L) for the particle length and sketch the graph of an (L), properly indicating ranges of values and corresponding units. [6 marks]