Question 3. A slurry of a seaweed is to be leached with hot water to recover a valuable protein. The slurry (48.1 % solids, 49% water and 2.9% protein) enters a countercurrent leaching battery at a rate of 400 kg/h. Hot water enters at the other end at a rate of 500 kg/h. The underflow leaving the unit may have a maximum of 0.2% protein. Calculate the number of ideal contact stages required. The following 'equilibrium data generated by laboratory tests may be used. Extract (overflow) concentration, mass fraction Water Protein Solids Slurry (underflow) concentration, mass fraction Water Protein Solids 0.952 0.967 0.979 0.989 0.046 0.032 0.021 0.011 0.002 0.001 0.00 0.00 0.00 0.00 0.542 0.564 0.586 0.5954 0.5994 0.432 0.417 0.401 0.026 0.019 0.013 0.0066 0.0036 0.0012 0.398 0.006 0.397 0.994 0.998 0.002 0.6028 0.396

Page No:1Fig(i): stage diagram for multi stage cocurrent leaching.Calculation procedurecalculate the weight ratio of solids to total kquid and the weight concent ration of protein on a solids broe basis for each of the two phase in eachrun of the experimental data.let No and Nu designate the weight ratios of solids to total liquid in the overtlow and underslow phases, respectively. similarly let no and ru nepresent the weight concentration of proteins on a solidsfree basis in the overblow and underblow phases, respectively . For ront, for instance.\begin{array}{l}N_{0}=\frac{0.002}{0.952+0.0456}=0.002 . \\N_{u}=\frac{0.432}{0.542+0.026}=0.760 \\n_{0}=\frac{0.046}{0.952+0.046}=0.046 . \\n_{u}=\frac{0.026}{0.542+0.026}=0.046\end{array}The calculated results for all ouns are as tollows (the sequenco being rearranged for convenience in step2):page NO:22. plot the equilibrium data. weight concentration of protein (solid-treebasis), n3. calculate the mean values for x and N.\begin{array}{l}n u=\frac{\left.l_{0} \omega_{p 0}+s_{N+1} e_{p, N+1}\right)}{l_{0}\left(w_{p, 0+} \omega_{\omega, 0}\right)+s_{N+1}\left(e_{p, N+1}+e_{\omega_{1} N+1}\right)} \\N_{m}=\frac{L_{0} w_{s, 0}+s_{N+1} e_{S_{1} N+1}}{L_{0}\left(w_{p, 0}+w_{w_{1}, 0}\right)+s_{N+1}\left(e e_{1} N+1+e_{\omega_{1} N+1}\right)}\end{array}Here x_{m}= mean weight concentration of protein on a solid-free basis.\mathrm{Nm}= mean weight ratio of solids to tatal liquid.10= Feed rate of sea water slurng\omega p, 0, \omega_{\omega, 0}, \omega_{s, 0}= weight Fractions of protein, water and solids . inthe sea water slusy .S_{N+1}= Feed rate of the hot water .e_{p, N+1}, e_{w, N+1}, e_{s, N+1}= weight Fractions of protein, water and solids in the enterning hot water.\begin{aligned}x_{M} & =\frac{400(0.029+500(0)}{400(0.029+0.49)+500(0+1)} \\& =0.0164 . \\N_{m} & =\frac{400(0.481)+500(0)}{400(0.029+0.49)+500(0+1)}=0.272\end{aligned}page NO:3(alculation of conch of protein in the product entract coversiow) streamscalculatio the number of stages.calculate the values of x and N for each of the two enterning steams - Thus 5or the seawater slurry.\begin{array}{l}N_{L, O}=\frac{0.481}{0.49+0.029}=0.927 \\\text { and } x_{L, O}=\frac{0.029}{0.49+0.029}=0.0559 \text {. }\end{array}For the entering hot water N_{S}, N_{s+1} and x_{S}, N+1 both equalo, because the stream contains neither solids not protein.Now, the number of stages can be tound graphically plot 10 that is x=0.0559, N=0.927 ) and sidraw a line through them, and extend it downward. Similarly plot the point S N+1 that is x=0, N=0 and L N, draw a line through them, extend it downward. Designate the intersection of the two lines as \triangle.thank you!! ...