Potential Flow, Circular Loop. Neglecting viscosity for an air glow find VP, the radial acceleration ar, and thecirculation I (m²/s) (eqn. 6.89) about the circular loop given by r = 5m, for the following: (a) rigid body fluidrotation with V₁ = 5r; (b) the potential free vortex given by Y = 5 In r; (c) for which case (s), a and/or/b, can thepressure difference between the origin and any other point be determined using the Bernoulli equation? Note thatfor both flows, V, = 0. Ans OM: (a) 10² Pa/m; -10² m/s²; 10² m²/s; (b) 10-¹ Pa/m; -10¹ m/s²; -10¹ m²/sy→x Cauchy'sΣF )equation of motion : pDV/Dt =pg + VT (like paNewtonian viscous stress relations by the tensor relation :Ti j = - pôij + µ[Əvj/əxi + əvi/axj]where dij is the kroneker delta function (1 for i=T includes pressure and viscous surface forces.into Cauchy's equation, and assume constant viscosity, to get the Navier-Stokesvector eq'ns : pDV/DtPg -vp + μ^2 Vthe acceleration DV/Dtav/at+ (VV)V, whichfor steady state flow gives DV/Dt =(V.) V.Because (VV) V is a non-linear term on the LHS of the N-S equationReynolds NumberRepVL/μ, a measure of the ratio of inertial to viscous forces.: Patm10^5==N=N=; pwater 1000; pair 1.2; μwater 10^-3 N s/m^2; Hair 2 x 10^-5 N•s/m^2; g 9.8 m/s^2=j; 0 for i j );N

Given Data: Circular Loop case(a) Vθ=5rcase(b) ψ = 5 ln (r) Find: (a) ∇P (b) radial acceleration(c)…

Potential Flow, Circular Loop. Neglecting viscosity for an air glow find VP, the radial acceleration a,, and the circulation I (m²/s) (eqn. 6.89) about the circular loop given by r = 5m, for the following: (a) rigid body fluid rotation with Ve=5r; (b) the potential free vortex given by Y = 5 In r; (c) for which case (s), a and /or/ b, can the pressure difference between the origin and any other point be determined using the Bernoulli equation? Note that for both flows, V, = 0. Ans OM: (a) 10² Pa/m; -10² m/s²; 10² m²/s; (b) 10¹ Pa/m; -10¹ m/s²; -10¹ m²/s y.

Potential Flow, Circular Loop. Neglecting viscosity for an air glow find VP, the radial acceleration a,, and the circulation I (m²/s) (eqn. 6.89) about the circular loop given by r = 5m, for the following: (a) rigid body fluid rotation with Ve=5r; (b) the potential free vortex given by Y = 5 In r; (c) for which case (s), a and /or/ b, can the pressure difference between the origin and any other point be determined using the Bernoulli equation? Note that for both flows, V, = 0. Ans OM: (a) 10² Pa/m; -10² m/s²; 10² m²/s; (b) 10¹ Pa/m; -10¹ m/s²; -10¹ m²/s y.

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 5.8P

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