# PS05 - MECH 411 Introduction to Fluid Mechanics American...

This preview shows pages 1–5. Sign up to view the full content.

MECH 411 Introduction to Fluid Mechanics Dec 25, 2004 American University of Beirut, Fall 2004-2005 Handout # PS5 Problem Set 5 Solution Textbook: 5.30, 5.38, 5.45, 5.67, 3.150, 3.162, 3.175, 3.176 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Problem 5.30 Variables: [ τ ] = ML - 1 T - 2 , [ ρ ] = ML - 3 , [ μ ] = ML - 1 T - 1 , [Ω] = T - 1 , [ R ] = L , r ] = L . Wall shear stress τ w = f ( ρ,μ, Ω ,R, Δ r ). Using ( ρ, Ω ,R ) as repeating variables. Number of dimensionless groups = 6 - 3 = 3. Π 1 = τ w 1 2 ρ Ω 2 R 2 = C f Π 2 = Δ r R Π 3 = ρ Ω R 2 μ = Re Therefore, in dimensionless form, τ w 1 2 ρ Ω 2 R 2 = f p Δ r R , ρ Ω R 2 μ P 2
Problem 5.38 Variables: [ d ] = L , [ D ] = L , [ U ] = LT - 1 , [ ρ ] = ML - 3 , [ μ ] = ML - 1 T - 1 , [ Y ] = MT - 2 . The number of dimensionless groups is 6 - 3 = 3. Using D,ρ and U as the repeating variables, the following dimensionless groups are obtained: Π 1 = ρUD μ = Re Π 2 = d D Π 3 = ρU 2 D Y = We Therefore, the relation in dimensionless form is d D = f (Re , We) 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Problem 5.45 Model diferential equation For chemical reaction dynamics in a plug reactor is u ∂C ∂x = D 2 C ∂x 2 - kC - ∂C ∂t (a) The above equation is physically homogeneous so that all terms have the units oF s - 1 . Then k has the unit oF s - 1 and D has the unit oF m 2 /s . (b) De±ning u * = u/V , x * = x/L , and t * = t/ ( L/V ) then the above equation is written as V L u * ∂C ∂x * = D L 2 2 C ∂x * 2 - kC - V L ∂C ∂t * u * ∂C ∂x * = D V L 2 C ∂x * 2 - kL V C - ∂C ∂t * The pi groups that appear are D V L which is ratio oF mass difusion efect to inertia efect and kL/V which is the ratio oF reaction time scale to inertia time scale.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 10

PS05 - MECH 411 Introduction to Fluid Mechanics American...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online