QUESTION 4 As shown in the accompanying figure, an inverted conical tank (with radius R and height H ) is being used as the feed vessel in a lab-scale membrane filtration setup to evaluate the ability of microfiltration membranes to treat an oily wastewater. A gear pump is used to withdraw the wastewater from the bottom of the tank and send it to a SEPA cross-flow filtration system (made by Sterlitech; https://www.sterlitech.com/sepa-cf-cell.html) at a constant volumetric flow rate (Q). 90% of the flow sent to the filtration system is recycled back to the top of the conical tank; the remaining 10% passes thru the microfiltration membrane and is collected in a separate vessel via the filtrate line. a. Starting from a general mass balance equation for the conical tank, derive the appropriate equation for the change in liquid level (dh dzai/dt ). b. Solve the differential equation from part a) to get the correct expression for the liquid level in the tank as a function of time (i.e. hmank(t)); an important condition for you to include is that at the beginning of each filtration test the tank is filled with wastewater to the same height ( h0). c. Using Excel, make a nice plot of the wastewater level in the tank (in cm) as a function of time (in min) for the following conditions: Tank height (H)=30cm Tank radius (R)=12cm Height of wastewater at beginning of filtration test (h)=28cm Volumetric flow rate generated by gear pump (Q)=0.6L/min Active area of membrane (A)=140cm2