Question

An aqueous alkaline solution is 20 wt% NaOH and has a specific gravity of 1.222. It flows through a 5 inch diameter pipe at a rate of 20 gpm (gallons per minute).

A) What is the mean velocity of the solution in the pipe?

B) What is the mole fraction NaOH in the solution?

C) What is the molarity of NaOH in the solution?

D) The solution is for use in an oil refinery, where they like to use “barrels per day” for units of flow rate. What is the flow rate of the solution in barrels per day?

Answer 1

Part a

Volumetric flow rate

= 20 gpm x (0.00379 m3/gallon) x 1min/60s)

= 0.00126 m3/s

Area = 3.14/4 *( 5in)^2 x (0.0254m/in)^2

= 0.01266 m2

Volumetric flow rate = area x velocity

Velocity = Volumetric flow rate / area

= 0.00126 m3/s/(0.01266 m2)

= 0.099516 m/s = 5.97 m/min

= 0.099516 m/s x 1ft/0.305m = 0.326 ft/s = 19.57 ft/min

Part b

Mass flow rate of solution = volumetric flow x density

= 0.00126 m3/s x 1.222 x 1000 kg/m3

= 1.53972 kg/s

Mass flow of NaOH = 0.20 x 1.53972 kg/s = 0.307944 kg/s

Moles of NaOH = mass/molecular weight

= 0.307944/40 = 0.0076986 kmol/s

Mass flow of water = 0.8*1.53972 = 1.231 kg/s

Moles of water = 1.231/18 = 0.0683 kmol/s

Total Moles = 0.076087 kmol/s

Mole fraction of NaOH = moles of NaOH / total moles

= 0.0076986/0.076087

= 0.101

Part C

Molarity of NaOH = moles of NaOH / volume of solution

= 0.0076986 kmol / 0.00126 m3

= 6.11 x 1000 mol/m3 x 1m3/1000L

= 6.11 Mol/L

Part d

flow rate of the solution in barrels per day

= 20 gallon/min x 0.0238095 barrels/gallon x 1440min/day

= 685.7136 barrels/day