Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 15, Problem 18P
To determine
To sketch:
A structured 4-sided grid and coarse hybrid grid with 4-sided in the region and its advantages.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A periodic Kármán vortex street is formed when an uniform stream flows over a
circular cylinder (Figure Q4). By applying method of repeating variables or
Buckingham Pi's Theorem, determine a dimensionless relationship for Kármán vortex
shedding frequency (fx.) as a function of free-stream speed (V), fluid density (p), fluid
viscosity(u), and cylinder diameter (D).
Q4
V
D
Figure Q4
As shown in the following figure, vortices are shed from the rear of a bluff cylinder placed across
a flow. The vortices alternately leave the top and bottom of the cylinder, causing an alternating
force normal to the freestream velocity. The vortex shedding frequency, f, depends on the fluid
density p, width of the cylinder d, freestream velocity V, and fluid viscosity u.
(a) Use Buckingham Pi Theorem to develop a functional relationship for f. Use M, L, t as the
primary dimensional. Use p, V, and d as the repeating parameters.
(b) Vortex shedding occurs in standard air on two cylinders with a diameter ratio of 2.
Determine the velocity ratio for dynamic similarity, and the ratio of vortex shedding
frequencies.
-Vortices
V
How do you get from equation 3.1.1 to 3.1.5? I understand that yoy mutiply both sides by Ui, but I'm confused on the math that is done to bring Ui into the partial derivative. Please show all intermediate steps.
Chapter 15 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 15 - A CFD code is used to solve a two-dimensional (x...Ch. 15 - Write a brief (a few sentences) definition and...Ch. 15 - What is the difference between a node and an...Ch. 15 - Prob. 4CPCh. 15 - Prob. 5CPCh. 15 - Prob. 6CPCh. 15 - Prob. 7CPCh. 15 - Write a brief (a few sentences) discussion about...Ch. 15 - Prob. 9CPCh. 15 - Prob. 10CP
Ch. 15 - Prob. 11CPCh. 15 - Prob. 13CPCh. 15 - Prob. 14CPCh. 15 - Prob. 15CPCh. 15 - Prob. 16PCh. 15 - Prob. 17PCh. 15 - Prob. 18PCh. 15 - Prob. 19PCh. 15 - Prob. 20PCh. 15 - Prob. 21PCh. 15 - Prob. 22PCh. 15 - Prob. 23PCh. 15 - Prob. 24PCh. 15 - Prob. 25PCh. 15 - Prob. 26PCh. 15 - Prob. 27PCh. 15 - For each statement, choose whether the statement...Ch. 15 - Prob. 45CPCh. 15 - Gerry creates the computational domain sketched in...Ch. 15 - Think about modem high-speed, large-memory...Ch. 15 - What is the difference between mulugridding and...Ch. 15 - Suppose you have a fair) comp1c geometry and a CFD...Ch. 15 - Generate a computational domain and grid, and...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Convert the following boundary value problem into a system of linear equation [A]{y} = {b}(without coding), with the following boundary conditions: y” +5y' = x, y(0) = 1, y(10) = 7 with n = 5 2hf'(x) h²f"(x) 2h³ f(x) f(x-2h) -1 1 f(x) f(x+h) f(x+2) 0 1 -2 0 6 flx-h) -1 2 -4 1 1 -2 -4 1 1 Table 5.1. Coefficients of central finite difference approximations of 0(h)arrow_forwardA 1:30 model of a ship is made. The real ship has a hull length of 130 m and travels at 7.9 m/s. Find the fraude number. If there is a dynamic similarity and froude # criterion applies, what should the velocity of the mdoel ship be?arrow_forward3.1 Two-dimensional incompressible flow can also be simulated using the vorticity w and streamfunction , instead of using the velocity and pressure variables. The vorticity field can be related to the velocity variables through the curl operation Əv ди Əx ду and the velocity field (u, v) can be related to the streamfunction with მს ду 11== v== Using the continuity equation, show that 2² 2² + əx² Əy² მს əx =-w. (3.252) (3.253)arrow_forward
- Select the correct answerarrow_forwardAt a particular time, the polar coordinates of a point P moving in the x-y plane are r = 4 m, 0 = 0.5 rad, and their time derivatives are dr/dt = 8 m/s and d0 /dt the velocity P, (b) What are the cartesian components of the velocity %3D %3D -2 rad/s. (a) What is the magnitude of %3D P? mB Artarrow_forward3.1 Two-dimensional incompressible flow can also be simulated using the vorticity w and streamfunction , instead of using the velocity and pressure variables. The vorticity field can be related to the velocity variables through the curl operation U Əv Әх ду and the velocity field (u, v) can be related to the streamfunction with მს Əy du მს əx (3.252) Show that the pressure field can be recovered from the streamfunction using the pressure Poisson equation.arrow_forward
- The Laws of Physics are written for a Lagrangian system, a well-defined system which we follow around – we will refer to this as a control system (CSys). For our engineering problems we are more interested in an Eulerian system where we have a fixed control volume, CV, (like a pipe or a room) and matter can flow into or out of the CV. We previously derived the material or substantial derivative which is the differential transformation for properties which are functions of x,y,z, t. We now introduce the Reynold’s Transport Theorem (RTT) which gives the transformation for a macroscopic finite size CV. At any instant in time the material inside a control volume can be identified as a control System and we could then follow this System as it leaves the control volume and flows along streamlines by a Lagrangian analysis. RTT:DBsys/Dt = ∂/∂t ʃCV (ρb dVol) + ʃCS ρbV•n dA; uses the RTT to apply the laws for conservation of mass, momentum (Newton's Law), and energy (1st Law of…arrow_forwardThe Laws of Physics are written for a Lagrangian system, a well-defined system which we follow around – we will refer to this as a control system (CSys). For our engineering problems we are more interested in an Eulerian system where we have a fixed control volume, CV, (like a pipe or a room) and matter can flow into or out of the CV. We previously derived the material or substantial derivative which is the differential transformation for properties which are functions of x,y,z, t. We now introduce the Reynold’s Transport Theorem (RTT) which gives the transformation for a macroscopic finite size CV. At any instant in time the material inside a control volume can be identified as a control System and we could then follow this System as it leaves the control volume and flows along streamlines by a Lagrangian analysis. RTT:DBsys/Dt = ∂/∂t ʃCV (ρb dVol) + ʃCS ρbV•n dA; uses the RTT to apply the laws for conservation of mass, momentum (Newton's Law), and energy (1st Law of…arrow_forwardThe Laws of Physics are written for a Lagrangian system, a well-defined system which we follow around – we will refer to this as a control system (CSys). For our engineering problems we are more interested in an Eulerian system where we have a fixed control volume, CV, (like a pipe or a room) and matter can flow into or out of the CV. We previously derived the material or substantial derivative which is the differential transformation for properties which are functions of x,y,z, t. We now introduce the Reynold’s Transport Theorem (RTT) which gives the transformation for a macroscopic finite size CV. At any instant in time the material inside a control volume can be identified as a control System and we could then follow this System as it leaves the control volume and flows along streamlines by a Lagrangian analysis. RTT:DBsys/Dt = ∂/∂t ʃCV (ρb dVol) + ʃCS ρbV•n dA; uses the RTT to apply the laws for conservation of mass, momentum (Newton's Law), and energy (1st Law of…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning
Unit Conversion the Easy Way (Dimensional Analysis); Author: ketzbook;https://www.youtube.com/watch?v=HRe1mire4Gc;License: Standard YouTube License, CC-BY