By using the expression for the shear stress derived in class (and in BSL), show that the shear force on asphere spinning at a constant angular velocity in a Stokes’ flow, is zero.This means that a neutrally buoyant sphere (weight equal buoyancy force) that is made to spin in aStokes’ flow, will neither rise nor fall, nor translate in any preferential direction in the (x-y) plane. expressions for velocity are: v_r (r,θ)= U_∞ [1-3R/2r+R^3/(2r^3 )] cosθ v_θ (r,θ)= -U_∞ [1-3R/4r-R^3/(4r^3 )] sinθ Where v_r and v_θ are the radial and angle velocity, U_∞ is the velocity of fluid coming to sphere which very faar away from the sphere. And R is the radius of sphere.
By using the expression for the shear stress derived in class (and in BSL), show that the shear force on asphere spinning at a constant angular velocity in a Stokes’ flow, is zero.This means that a neutrally buoyant sphere (weight equal buoyancy force) that is made to spin in aStokes’ flow, will neither rise nor fall, nor translate in any preferential direction in the (x-y) plane. expressions for velocity are: v_r (r,θ)= U_∞ [1-3R/2r+R^3/(2r^3 )] cosθ v_θ (r,θ)= -U_∞ [1-3R/4r-R^3/(4r^3 )] sinθ Where v_r and v_θ are the radial and angle velocity, U_∞ is the velocity of fluid coming to sphere which very faar away from the sphere. And R is the radius of sphere.
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 5.3P: Evaluate the Nusselt number for flow over a sphere for the following conditions: D=0.15m,k=0.2W/mK,...
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Question
By using the expression for the shear stress derived in class (and in BSL), show that the shear force on a
sphere spinning at a constant angular velocity in a Stokes’ flow, is zero.
This means that a neutrally buoyant sphere (weight equal buoyancy force) that is made to spin in a
Stokes’ flow, will neither rise nor fall, nor translate in any preferential direction in the (x-y) plane.
expressions for velocity are:
v_r (r,θ)= U_∞ [1-3R/2r+R^3/(2r^3 )] cosθ
v_θ (r,θ)= -U_∞ [1-3R/4r-R^3/(4r^3 )] sinθ
Where v_r and v_θ are the radial and angle velocity, U_∞ is the velocity of fluid coming to sphere which very faar away from the sphere. And R is the radius of sphere.
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