The contents of a tank are to be mixed with a turbine impeller that has six flat blades. The diameter of the impeller is 3 m. If the temperature is 20°Cand the impeller is rotated at 30 rpm (rev/min), what will be the power consumption? Use power number (Np) of 3.5

P=3.31 hp (2.47 kW).

Explanation:

Solution

Curve A in Fig1. applies under the conditions of this problem.

S1 = Da / Dt ; S2 = E / Dt ; S3 = L / Da ; S4 = W / Da ; S5 = J / Dt and S6 = H / Dt

The above notations are with reference to the diagram below against the dimensions noted. The notations are valid for other examples following also.

32.2

Fig. 32.2 Dimension of turbine agitator

The Reynolds number is calculated. The quantities for substitution are, in consistent units,

D a =2⋅ft

n= 90/ 60 =1.5 r/s

μ = 12 x 6.72 x 10-4 = 8.06 x 10-3 lb/ft-s

ρ = 93.5 lb/ft3 g= 32.17 ft/s2

NRc = (( D a) 2 n ρ)/ μ = 2 2 ×1.5×93.5 8.06× 10 −3 =69,600

From curve A (Fig.1) , for NRc = 69,600 , N P = 5.8, and from Eq. P= N P × (n) 3 × ( D a )5 × ρ g c

The power P= 5.8×93.5× (1.5) 3 × (2) 5 / 32.17 =1821⋅ft−lb f/s requirement is 1821/550 = 3.31 hp (2.47 kW).