Question 7.P.3: Compare the capital and operating costs of a three-bladed pr...
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.
The capital cost of an impeller, C=F_M C_B P ^n
where F_M is a factor for the material of construction which for mild steel =1.0, C_B is a base cost £, P is the power (kW) and n is an index (-).
For the propeller: C_B=960 £(1990) and n = 0.34
∴ C=\left(1.0 \times 960 \times 1^{0.34}\right)=£ 960
\left.\begin{array}{l} \text{Interest and depreciation}=(960 \times 15 / 100)=£ 144 / \text { year } \\\text{Operating costs}=(1 \times 0.01 \times 8000)=£ 80 \text { /year }\end{array}\right\} \text { a total of } \underline{\underline{£ 224 / \text { year }}}For the turbine: C_B=3160 £(1990) and n = 0.10
∴ C=\left(1.0 \times 3160 \times 1^{0.10}\right)=£ 3160
\left.\begin{array}{l} \text{Interest and depreciation}=(3160 \times 15 / 100)=£ 474 / \text { year } \\\text{Operating costs}=(1 \times 0.01 \times 8000)=£ 80 \text { /year }\end{array}\right\} \text { a total of } \underline{\underline{£ 554 / \text { year }}}In equation 7.13, k^{\prime}=165 for a propeller and 3245 for a turbine.
For the propeller: P =165 N^3 D^5
or: 1000=165 N^3 0.3^5 and N=\underline{\underline{13.5 Hz }} (810 rpm )
For the turbine: P =3245 N^2 D^5
or: 1000=\left(3245 N^3 0.45^5\right) and N=\underline{\underline{2.54 Hz }} (152 rpm )