Buckingham Pi. Experiments show that the coefficient of drag CD = F/(1/2 pAV^2) for smooth spheres should only be a function of a Reynold's number (Re=pVD/μ). Here F is the total drag force of the fluid on the sphere and includes all the viscous and pressure forces; and A is the frontal area, A = pi * D^2 /4. The drag force on small spheres (D=0.3cm) in air at V = 12m/s is to be predicted using experimental results for a larger sphere (D=0.9cm) in water. (a) What experimental water speed is required? (b) what will be the ratio of drag forces (Fwater/Fair)? (c) for very small spheres it is known that Cd = 24/Re. It is observed that two very small rain drops falling in air have a terminal speed ratio of V2/V1 = 4. What would be the ratio of the rain drop diameters (D2/D1)? SI constant Patm = 10^5 Pa; pwater ~ 1000 kg/m^3; pair - 1.2kg/m^3; µwater - 10^-3 N•s/m^2; pair - 2 x 10^-5 N•s/m^2; g = 9.8 m/s^2 the terminal speed is reached when the drop weight equals the drag force; air buoyancy force can be neglected. unit expecting: (a) Vw: 10^-1 m/s; (b) Fw/Fa: 10^0; (c)D2/D1: 10^0
Buckingham Pi. Experiments show that the coefficient of drag CD = F/(1/2 pAV^2) for smooth spheres should only be a function of a Reynold's number (Re=pVD/μ). Here F is the total drag force of the fluid on the sphere and includes all the viscous and pressure forces; and A is the frontal area, A = pi * D^2 /4. The drag force on small spheres (D=0.3cm) in air at V = 12m/s is to be predicted using experimental results for a larger sphere (D=0.9cm) in water. (a) What experimental water speed is required? (b) what will be the ratio of drag forces (Fwater/Fair)? (c) for very small spheres it is known that Cd = 24/Re. It is observed that two very small rain drops falling in air have a terminal speed ratio of V2/V1 = 4. What would be the ratio of the rain drop diameters (D2/D1)? SI constant Patm = 10^5 Pa; pwater ~ 1000 kg/m^3; pair - 1.2kg/m^3; µwater - 10^-3 N•s/m^2; pair - 2 x 10^-5 N•s/m^2; g = 9.8 m/s^2 the terminal speed is reached when the drop weight equals the drag force; air buoyancy force can be neglected. unit expecting: (a) Vw: 10^-1 m/s; (b) Fw/Fa: 10^0; (c)D2/D1: 10^0
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Transcribed Image Text:Buckingham Pi. Experiments show that the coefficient of drag CD = F/(1/2 pAV^2) for smooth spheres should only be a function of a Reynold's number
(Re=pVD/μ). Here F is the total drag force of the fluid on the sphere and includes all the viscous and pressure forces; and A is the frontal area, A = pi
* D^2 /4. The drag force on small spheres (D=0.3cm) in air at V = 12m/s is to be predicted using experimental results for a larger sphere (D=0.9cm) in
water. (a) What experimental water speed is required? (b) what will be the ratio of drag forces (Fwater/Fair)? (c) for very small spheres it is known that Cd
= 24/Re. It is observed that two very small rain drops falling in air have a terminal speed ratio of V2/V1 = 4. What would be the ratio of the rain drop
diameters (D2/D1)?
SI constant Patm = 10^5 Pa; pwater ~ 1000 kg/m^3; pair - 1.2kg/m^3; µwater - 10^-3 N•s/m^2; pair - 2 x 10^-5 N•s/m^2; g = 9.8 m/s^2
the terminal speed is reached when the drop weight equals the drag force; air buoyancy force can be neglected.
unit expecting: (a) Vw: 10^-1 m/s; (b) Fw/Fa: 10^0; (c)D2/D1: 10^0
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