Hi, I am brand new to chemical engineering and am attaching the problem that I need help with. Thank you for any guidance or step-by-step process you can offer.
3. b) A rotary ﬁlter is used to deposit a solid cake on the outside of a rotating porous belt bycontinuously pulling a vacuum through the belt. The ﬁlter rotates at an angular velocity 9and has a radius R. The solution subtends an angle 14; as shown in the ﬁgure. The purpose of this problem is to construct a model equation to predict the rate of solid product fed to theconveyer belt as a ﬁlnction of the system parameters. Assume that the bottom slurry pan of the ﬁlter contains a uniform suspension of the solid atconcentration Cs g solid/cm3. The porous belt on the ﬁlter may be assumed to be a perfect ﬁlter, i.e., no solid is passed through the belt. The permeation velocity vp (cm/s) through theﬁlter cake is given by Darcy’s law v k‘ 2 APp 6+t Where In and 5 are constants, Ap is the pressure drop across the ﬁlter cake which is constantand t is the thickness of the cake. You may assume that the cake is deposited at a constant porosity e. Derive by a shell balance the differential equation that governs the thickness of the cake as aﬁlnction of the angle 9. From the solution to the model equation developed in (a) show how to calculate the amountof solid produced as a ﬁmction of operating and system parameters. Feed Slurry Q; :9I/ \0Solution Level Return toslurry tank Conveyor to dryer