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

Question

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.

Accepted Answer

The capital cost of an impeller, [latex]C=F_M C_B P ^n[/latex]
where [latex]F_M[/latex] is a factor for the material of construction which for mild steel [latex]=1.0, C_B[/latex] is a base cost £, P is the power (kW) and n is an index (-).
For the propeller: [latex]C_B=960 £(1990)[/latex] and n = 0.34

∴ [latex]C=\left(1.0 imes 960 imes 1^{0.34} ight)=£ 960[/latex]

[latex]\left.\begin{array}{l} ext{Interest and depreciation}=(960 imes 15 / 100)=£ 144 / ext { year } \ ext{Operating costs}=(1 imes 0.01 imes 8000)=£ 80 ext { /year }\end{array} ight\} ext { a total of } \underline{\underline{£ 224 / ext { year }}}[/latex]

For the turbine: [latex]C_B=3160 £(1990)[/latex] and n = 0.10

∴ [latex]C=\left(1.0 imes 3160 imes 1^{0.10} ight)=£ 3160[/latex]

[latex]\left.\begin{array}{l} ext{Interest and depreciation}=(3160 imes 15 / 100)=£ 474 / ext { year } \ ext{Operating costs}=(1 imes 0.01 imes 8000)=£ 80 ext { /year }\end{array} ight\} ext { a total of } \underline{\underline{£ 554 / ext { year }}}[/latex]

In equation [latex]7.13, k^{\prime}=165[/latex] for a propeller and 3245 for a turbine.
For the propeller: [latex]P =165 N^3 D^5[/latex]

or: [latex]1000=165 N^3 0.3^5[/latex] and [latex]N=\underline{\underline{13.5 Hz }}[/latex] (810 rpm )

For the turbine: [latex]P =3245 N^2 D^5[/latex]

or: [latex]1000=\left(3245 N^3 0.45^5 ight)[/latex] and [latex]N=\underline{\underline{2.54 Hz }}[/latex] (152 rpm )

Question 7.P.3: Compare the capital and operating costs of a three-bladed pr...

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