As part of the initial treatment for waste water from an industrial site, you wi
ID: 2001013 • Letter: A
Question
As part of the initial treatment for waste water from an industrial site, you will be running the afluent through a sand filter. The filtering ability of the sand in this filter is roughly proportional to the surface area of the sand enclosed. The grains of fine sand are approximately spheres with an average radius of 50 m and are made of silicon dioxide. A solid cube of this material with a volume of 1 m3 has a mass of 2550 kg. You have determined that the total surface area (the total area of all the individual grains) is equal to the surface area of a cube 0.8 meters on an edge.
1) What mass of sand grains needed for your filter?
Explanation / Answer
The required surface area of grained sand is the same as surface area of the cube, that is A=6*0.8*0.8=3.84 m^2;
The surface area of a grain is a=4*pi*r^2, where r=50e-6 m;
thus number of grains required is n=A/a =A/(4*pi*r^2);
Volume of a grain is v=(4/3)*pi*r^3;
the volume of sand required is V=n*v;
the mass of sand is m=V*p, where p=2550 kg/m^3;
Thus m=n*v*p = (A/(4*pi*r^2))* (4/3)*pi*r^3 *p =(A/3)*r*p =(3.84/3)*50e-6*2550 =0.1632 kg
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