Practice questions

<rst> <rst-options: 'toc' = False/> <rst-options: 'reset-figures' = False/>

.. |-| replace:: :math:`-` .. |+| replace:: :math:`+` .. |micron| replace:: :math:`\mu \text{m}`

.. question::

A sample of material was settled in a graduated lab cylinder 300mm tall. The interface dropped from 500mL to 215mL on the graduations during a 4 minute period.

#. Give a preliminary estimate of the clarifier diameter required to treat a waste stream of 2100 L per minute. Over-design by a factor of 2, based on the settling rate, and account for about 7 $\text{m}^2$ of entry area used to eliminate turbulence in the entering stream. #. If the feed concentration is 3.5 kg per $\text{m}^3$ feed, what is the loading rate? Is it within the typical thickener range of 50 to 120 kg per day per square meter (Perry, 8ed, p22-79)?

.. answer::

#. Settling rate = 171 mm per 4 minutes = 42.8 mm/min.

Area = :math:`\displaystyle \frac{2.1~\text{m}^3.\text{min}^{-1}}{\left(\frac{1}{2}\right)\left(42.8 \times 10^{-3} \text{m}.\text{min}^{-1}\right)} = 98 + 7 \text{m}^2`

#. :math:`\psi = C_0 v = 3.5 \displaystyle\frac{\text{kg}}{\text{m}^3} \cdot 0.022 \displaystyle \frac{\text{m}}{\text{min}} \cdot \displaystyle\frac{60 \times 24 \text{min}}{\text{day}} = 106 \displaystyle \frac{\text{kg}}{\text{day}.\text{m}^2}`

.. question::

#. Calculate the minimum area and diameter of a circular thickener to treat 720 :math:`\text{m}^3` per hour of slurry containing 20 |micron| particles of silica, whose density is about 2600 :math:`\text{kg.m}^{-3}`. The particles are suspended in water at a concentration of 650 :math:`\text{kg.m}^{-3}`. The slurry cannot be tested in a lab. Use an over-design factor of 1.5 on the settling velocity. #. If it is desired to have an underflow concentration of 1560 kg solids per :math:`\text{m}^{3}` underflow; what is the underflow volumetric flow rate if total separation of solids occurs? #. Calculate the separation factor. </rst>