Buckingham Pi. A mechanical stirrer is used to mix chemicals in a large tank. The required shaft power P is a function of liquid density p, viscosity μ, stirrer blade diameter D, and angular speed w of the spinning blades. (a) use repeating variables p, D, u to find a relation between dimensionless power (1) and w (n2); (b,c) a small 1/3 scale model is used in water to predict the actual required power in a viscous liquid with SG =2 and μ = 12μwater. Find (b) the ratio of speeds, wwater/ wactual, necessary for dynamic similarity and then (c) the predicted ratio of powers Pwater/ Pactual. = expecting unit: (a) π1 - D; π^2 - D^2; (b) wwater/ wactual: 10^0; (c) Pwater/ Pactual = 10^-3 SI constant Patm = 10^5 Pa; pwater - 1000 kg/m^3; pair ~ 1.2kg/m^3; μwater - 10^-3 N•s/m^2; Hair - 2 x 10^-5 Nes/m^2; g = 9.8 m/s^2

Buckingham Pi. A mechanical stirrer is used to mix chemicals in a large tank. The required shaft power P is a function of liquid density p, viscosity μ, stirrer blade diameter D, and angular speed w of the spinning blades. (a) use repeating variables p, D, u to find a relation between dimensionless power (1) and w (n2); (b,c) a small 1/3 scale model is used in water to predict the actual required power in a viscous liquid with SG =2 and μ = 12μwater. Find (b) the ratio of speeds, wwater/ wactual, necessary for dynamic similarity and then (c) the predicted ratio of powers Pwater/ Pactual. = expecting unit: (a) π1 - D; π^2 - D^2; (b) wwater/ wactual: 10^0; (c) Pwater/ Pactual = 10^-3 SI constant Patm = 10^5 Pa; pwater - 1000 kg/m^3; pair ~ 1.2kg/m^3; μwater - 10^-3 N•s/m^2; Hair - 2 x 10^-5 Nes/m^2; g = 9.8 m/s^2

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.9P: When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the...

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