Question

Assume that the water temperature is 10°C and the depth of the settling tank is 3.0 m. Calcium carbonate precipitates with a relative density of 1.20 and diameter of 0.10 mm to be removed in a settling tank after softening treatment. Assume discrete particle settling. At 10°C the density and viscosity of water are 999.77 kg/m3 and 1.308x10-3 kg/m.s.

a. Calculate the theoretical settling velocity (cm/s), tank loading (m3 /m2 /d) and detention time (h) required for the removal.  

b. How will the settling velocity change, if the viscosity, particle diameter, and the relative density increases by 10%? How will the settling velocity change if the water temperature is 25 oC instead of 10 oC? Vary only one parameter at a time. Comment; no need to provide calculations.

Answer 1

Reynolds number = 10

So,we can find drag coefficient for this range of reynolds number

As we know that terminal velocity is given by

So,we get

Tank loading,L

V_water is volumetric flow of water being treated

Now finding detention time

b.)

Settling velocity is given by

Where

If viscosity increases by 10% then reynolds number will decrease,due to which drag coefficient,C_D will increase ,as C_D will decrease ,settling velocity will increase

. If particle diameter will increase by 10% ,then terminal velocity will increase as m_p(mass of particle will increse as we increase diameter of particle)

. If relative density of particle will increase ,then difference of (-) will also increase, hence terminal velocity will also increase

. If temperature of water is increased,then its density will decrease due to relative density of particle will also decrease with it, hence net effect on terminal velocity will depend upon the value of density of water and particle at that temperature ,as