A 5.00 wt% aqueous sulfuric acid solution (rho = 1.03 g/ml) flows through a 45-m

Question

A 5.00 wt% aqueous sulfuric acid solution (rho = 1.03 g/ml) flows through a 45-m long pipe with a 6.0 cm diameter at a rate of 82 L/min. What is the molarity of sulfuric acid in the solution? How long (in seconds) would it take to fill a 55-gallon drum, and how much sulfuric acid (lb_m) would the drum contain? You should arrive at your answers with two dimensional equations.) The mean velocity of a fluid in a pipe equals the volumetric flow rate divided by the cross-sectional area normal to the direction of flow. Use this information to estimate how long (in seconds) it takes the solution to flow from the pipe inlet to the outlet.

Explanation / Answer

(a)

Sulfuric acid (H2SO4) Molecular weight =98.08 g/mol

=1.03 gm/ml =1030 gm/lit

Now 5 wt% sulfuric acid solution

So in 100 gm of solution 5 gm of sulfuric acid.

So Molarity = (5 gm sulfuric acid/ 100 gm solution)*1030 gm/lit /98.08 (gm/mol) = 0.525 mol/lit

(b)

1 lit=0.264 gal

Rate = 82 lit/min *0.264 gal/lit *(min /60 sec) =0.3608 gal/sec

So time =55 gal /0.3608 (gal/sec) =152.43 sec

= 1030 gm/lit *(lit/0.264 gal)*(1lbm/453.6 gm)=8.6012 lbm/gal

So 55 gal*8.6012 lbm/gal=473.067 lbm

(c)

A=D2/4 =3.14*62/4 =28.26 cm2

Now rate =82 lit/min =82000 cm3/min=1366.67 cm3/sec

Now we know that

velocity=V=rate/Area =Q/A=1366.67/28.26=48.36 cm/sec =0.4836 m/sec

Time = 45 m /0.4836 m/sec =93.05 sec

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