SO2 is removed from the combustion product stream of coal by

SO2 is removed from the combustion product stream of coal by dissolving (absorption) into a water stream. Water at 25 C flows down the inside surface of a vertical column by gravity only, with inner diameter of 0.5 m. To facilitate absorption, it has been determined that the film should be kept at 4 mm thick with laminar flow. The column height is 10 m. Calculate the maximum volumetric flow rate of water (in m3/s) that can flow through the column under the given conditions.

*********note that film thickness is much much smaller than column diameter.

Assume that the film is isothermal at 25 C.

Solution

Given:

1. Diameter of cylinderical shell = 0.5 m

2. Height of cylindrical shell = 10 m

3. Flow category = Laminar under gravity

4. Isothermal process at 25 deg C

Since the flow is laminar, the shearing forces are not dominating and water flows smoothly.

For any flow, Reynolds number is an important parameter to determine.

Re = mean velocity of fluid * hydraulic dia / kinematic viscosity of fluid - 1

Also,

Re = (Volumetric flow of fluid * hydraulic dia) / (kinematic viscosity of fluid * Area of cross section of column) - 2

Solving 1 and 2

we get,

Volumetric flow rate (Q) = MEan velocity of fluid (v) * Cross sectional area

Cross sectional area of column = 3.14 * 0.5 * 0.5 / 4 = 0.19625 m2

Since, water is fowing under gravity,

assuming initial velocity = 0 m/sec

acceleration = 10 m /s2

distance = height of column = 10

we get,

s = u*t + 1/2*a*t*t

10 = 0 + 1/2*10*t*t

t = sqrt (2) sec

final velocity of fluid at end of column = 10*sqrt (2) = 14.14 m /sec

mean velocity of fluid = (14.14 + 0) / 2 = 7.07 m/sec

Volumetric flow rate = Q = 7.07 * 0.19625 m3 /sec

= 1.387 m3 / sec

~ 1.4 m3/sec