Paddle Flocculator Power from Geometry

ScopeP = 0.5 x Cd x rho x A x v_rel^3, the Newtonian drag. Two subtleties - the power goes as the CUBE of the relative velocity, and the water slips (rotates with the paddles) so v_rel is only (1 - k) of the tip speed; ignoring the slip overstates the power by 1/(1 - k)^3, about 2.4x at k = 0.25 and 4.6x at k = 0.40. A wheel with paddles at a 6 ft radius, turning at 3 rpm with 40 ft^2 of blade, delivers ~267 W. Cd (~1.8) and slip k (~0.25) are user inputs because references disagree; the drag is exact once chosen. A design aid, not a metered power.

Formula or tablev_tip = 2 x pi x paddle_radius_ft x wheel_rpm / 60; v_rel = v_tip x (1 - slip_factor); power_ftlbs = 0.5 x drag_coeff x 1.937 x paddle_area_ft2 x v_rel^3; power_w = power_ftlbs x 1.35582; power_hp = power_ftlbs / 550.

Source and editionCamp paddle flocculator power (water-treatment design practice), by name.

Free accessThe Camp paddle-power drag relation is public water-treatment design material; the flocculator design and the operator govern.

What governsEstimate. AHJ and licensed professional govern.

API field namespaddle_radius_ft, wheel_rpm, paddle_area_ft2, drag_coeff, slip_factor, v_rel_fps, power_ftlbs, power_w

• Cube law and slip P scales with v_rel^3, and v_rel = (1 - k) x tip speed; ignoring the slip overstates the power by 1/(1 - k)^3, about 2.4x at k = 0.25 and 4.6x at k = 0.40Camp / water-treatment design practice
• User-chosen constants Cd (about 1.8, 1.0-1.8 reported) and k (about 0.25, 0.25-0.40 reported) are inputs because the references disagreeflocculation literature