CHEMICAL ENGINEERING

104 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

PROBLEM 7.3

Compare the capital and operating costs of a three-bladed propeller with those of a constant

speed six-bladed turbine, both constructed from mild steel. The impeller diameters are

0.3 and 0.45 m respectively and both stirrers are driven by a 1 kW motor. What is the

recommended speed of rotation in each case? Assume operation for 8000 h/year, power

costs of £0. 01 /kWh and interest and depreciation at 15%/year.

Solution

The capital cost of an impeller,CDFMCBPn

whereFMis a factor for the material of construction which for mild steelD 1 .0,CBis a

base cost£,Pis the power (kW) andnis an index ().

For the propeller:CBD960£ 1990 andnD 0. 34

∴ CD 1. 0 ð 960 ð 10.^34 D£960

Interest and depreciationD 960 ð 15 / 100 D£144/year
Operating costsD 1 ð 0. 01 ð 8000 D£80/year

}

a total of £224/year

For the turbine:CBD3160£ 1990 andnD 0. 10

∴ CD 1. 0 ð 3160 ð 10.^10 D£3160

Interest and depreciationD 3160 ð 15 / 100 D£474/year

Operating costsD 1 ð 0. 01 ð 8000 D£80/year

}

a total of £554/year.

In equation 7. 13 ,k^0 D165 for a propeller and 3245 for a turbine.

For the propeller:PD 165 N^3 D^5

or: 1000 D 165 N^30. 35 andND 13 .5Hz(810 rpm)

For the turbine:PD 3245 N^2 D^5

or: 1000 D 3245 N^30. 455 andND 2 .54 Hz(152 rpm)

PROBLEM 7.4

In a leaching operation, the rate at which solute goes into solution is given by:

dM/dtDkcsckg/s

whereMkg is the amount of solute dissolving ints,km^3 /sis a constant andcsandc

are the saturation and bulk concentrations of the solute respectively in kg/m^3. In a pilot

test on a vessel 1 m^3 in volume, 75% saturation was attained in 10 s. If 300 kg of a solid