A$2$

Water is $91\mathrm{.}4\%$ saturated. Water flows through a packed bed of $5mm$ diameter calcium carbonate spheres at a

superficial velocity of $325cm*s^{-1}.$ The water is initially pure and for this operation, the mass

transfer coefficient of calcium carbonate into water, $k((m)*s^{-1}),$ is given by the following

relationship:

$k=1\mathrm{.}17V(\frac{dV}{v}{)}^{-0\mathrm{.}42}(\frac{D}{v}{)}^{\frac{2}{3}}$

where $D$ is the diffusion coefficient $(m^2.s^{-1})$ of calcium carbonate into water, $V$ is the liquid

superficial velocity $($m$.s^{-1}),v$ is the liquid viscosity $($Pa$.$s$)$ and $d$ is the particle diameter $($m$).$

Determine the percentage saturation of the water after passing through a bed height of

$20cm$ if the water viscosity is $1\mathrm{.}5{10}^{-5}Pa.$s and the diffusion coefficient is $1{10}^{-6}{m}^2*s^{-1}$

ANS : WATER IS $91\mathrm{.}4\%$ SATURATED