Question

Our company makes biodiesel using a process that reacts waste oil from fast food friers (the reaction used is called a transesterification). The reaction occurs between two immiscible liquid phases, a hydrophobic organic and an aqueous phase. Once the reaction is complete, we let the emulsion separate and wish to drain the aqueous phase from the bottom, keeping the biodiesel at the top.

TimehhAhBBiodieselAqueousPhaseBiodieselEmulsion

Before we open the valve at the bottom of the tank to drain the aqueous phase, we wish to estimate the pressure, for safety reasons. The total height of liquid in the settling tank is 15.000 m, and we measure a height of 3.290 m for the aqueous phase. If the density of our aqueous phase is 1.1800 g/ml and the density of our biodiesel is0.8880 g/cm³, what is the gauge pressure at the at the bottom of the tank?

(HINT: |X| is near an order of magnitude of 10² kPa ).

Answer 1

Density of biodiesel is lower than density of aqueous phase so biodiesel will be at top and aqueous phase will be at bottom because both phases are immiscible

Now height of biodiesel =15-3.29 =11.71 m

We know for a top pressure of P1 ang height h, bottom absolute pressure (P2)= P1+Rho*g*h

Now for gauge pressure =P2-P1 = Rho*g*h

We need to apply above equation for both phases corresponding to their heights and density

We know 1 gm/ml =1000 kg/m3

Gauge pressure =( 11.71*9.8*0.888 +3.29*9.8*1.18)*1000

= 139.95 kPa