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Unformatted text preview: Chemical Engineering 374
Fluid Mechanics Fall 2010
Exam 2 Review 1 Exam Review, By Content/Lectures Classes 13-21 Chapter 5.6 Chapter 7.1-7.5 Chapter 8.1-8.8 Laminar Turbulent Minor Losses Single Pipelines Pipe networks Flow measurement 2 Mechanical Energy Dimensional Analysis Pipe Flows 1 Class 13--Mechanical Energy Mechanical Energy Balance Steady state Friction losses included but just given What if have heat transfer? Head form? v 2 P + + gz 2 3 = W F - m m ME changes due to shaft work and friction KE correction factor Know this, but ignore unless stated (i.e., exam), or laminar Examples similar to Chp 8, where we compute the friction losses explicitly. Class 14--Dimensional Analysis Dimensional Homogeneity Nondimensionalize equations: t*=t/tref; t=(tref)(t*) Scaling Terms in equations become product of [..](..), where [..] give size, (..) is O(1). Can use this to find functional forms. Heat equation characteristic time Boundary layer thickness. 4 Similarity--3 types (geometric, kinematic, dynamic) Equivalent systems are similar The groups need to be equal between model and full-scale 2 Class 15--Dimensional Analysis Find dimensionless groups ('s) 3 methods: governing equations, force ratios, method 5 method is general (but can be cumbersome) n parameters j dimensions k=n-j 's Fluids, usually have 3 dimensions (m, s, kg) Can usually guess the 's directly Use all parameters Helps to pick j=n-k repeating parameters that appear in all 's Re is common in fluids with viscous effects (friction, drag, etc.) Class 16--Laminar Pipe Flow Pipe discussion More on the Re (physical intuition: Force ratio, timescale ratio) Re < 2300 is laminar; Re > 4000 is turbulent (transition in between) 2300 is the number to remember as the laminar/turbulent cutoff Most flows are turbulent 6 Hydraulic diameter (for noncircular pipes) Dh=4Ac/Pw Entrance region Fully developed flow takes time/space Wall stress/friction/pressure drop is higher in entrance region. Derive the velocity profile Force balance ODE (pressure, wall friction) (BC: v=0 at wall, dv/dx=0 at CL) 2 integrations parabolic profile dp/dx is constant vavg = vmax (for circular pipes!) 4w f 2 f defined, f = 64/Re v /2 3 Class 17--Turbulent Flow Darcy friction factor: f = 8w/vavg2 PL/= fLv2/2D f = 4 * fFanning 7 Velocity profile is flatter, with steep wall gradients higher wall friction higher friction than laminar. Power law velocity profiles available Pipe roughness is important due to thin viscous wall layer. Params are P, L, , , , D, v 3 's f(Re, /D) Colbrook equation (implicit) Haaland equation Moody chart Note simplifications: rough pipes at high Re f is constant (read off Moody, or simple Colbrook) Smooth pipes give a simpler Colbrook equation Class 18--Minor Losses Losses from fittings, bends, valves, etc. In a pipe of a given size, use KL Table 8-4 Based on the smaller of two diameters Use loss coefficient or equivalent lengh and add to pipe length. Don't forget expansions! K=1 (K=). Contractions vena contracta Valves increase friction to decrease flow rate for given pressure difference. 8 4 Class 19--Single Pipelines 9 Note well the mechanical energy balance equation above with shaft (pump) work, pipe losses, and minor losses. Three problem types. Find P, find V, find D Some require iteration. Know how to do this to solve the three types. Find V : Guess f, v from E eqn., get Re, get f=f(Re, e/D), repeat. Find D : Guess D, get Re, get f=f(Re,e/D), D from E. eqn, repeat. System demand curve can turn a harder type into an easy type to "bypass" iteration. Examples given Economic pipe diameter (velocity), pipe size charts. Class 20--Pipe Networks 2 Key parameters: P, V Series Flow Ptot = Pi Constant V 10 Parallel Flow
Vtot = Vi Pi =Pj=Pk For pipes between the same two nodes Type 1 (find P) and 2 (find V ) problems considered A system demand curve can help conceptually (and computationally) Can also set up and solve system of nonlinear equations More complex networks are the sum of the parts Qi=0 at "nodes" (pipe junctions) Pi=0 around loops. Like Kirchoff's laws for current flow (but nonlinear) 5 Class 21--Flow Measurement Flow meter types discussed Emphasis on Bernoulli types Pitot, Pitot-static Orifice meters Nozzles Venturi meters 11 Rotameters Discharge coefficient correlations provided Require iteration, but good guesses given low variation of Cd Book provides average values (their values agree better with correlations at lower Re) 0.61, 0.96, 0.98 for orifice, nozzle, venturi, respectively 6 ...
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This note was uploaded on 03/11/2012 for the course CHE 374 taught by Professor Davidlignell during the Fall '12 term at Brigham Young University, Hawaii.
- Fall '12
- Chemical Engineering